How do LDS know that Brigham Young and his successors are true prophets?

Question

Many LDS have a testimony that Joseph Smith Jr was a true prophet. Let us suppose someone studies the life and teachings of Joseph Smith, and reaches the conclusion that he is a true prophet. But, to accept the present day mainstream LDS church, surely it is not just necessary to accept Joseph Smith as a true prophet, but that also Brigham Young was the correct successor of Joseph Smith (as opposed to say Joseph Smith III - as the RLDS/Community of Christ believe, or James Strang, or Sidney Rigdon, or Granville Hedrick, or Alpheus Cutler.)

Furthermore, in addition to accepting Brigham Young as Joseph Smith's rightful successor, one must also accept that all the subsequent successors of Brigham Young as President of the LDS Church are his rightful successors, rather than any of them having fallen into apostasy (as many of those who practice plural marriage claim.)

1. So my question then is, do you agree, that to become LDS, it is not enough to just have a testimony about the prophecy of Joseph Smith, but also about Brigham Young and successors?
2. How in practice do LDS members go beyond a testimony about Joseph Smith to a testimony about Brigham Young and his successors also?
3. How does one know that the LDS church headquartered in Salt Lake City is the true successor to the church founded by Joseph Smith Jr, as opposed to say the Community of Christ or the Church of Christ Temple Lot?

Answer 1

Members of the Church of Jesus Christ of Latter Day Saints are encouraged to get a testimony of each of those prophets.

1.I don't disagree with you. However, I would think that a testimony of the current prophet, would be enough. If you know the first to be true, and today's to be true that should be enough. If you decide that one in the middle isn't a true prophet, but you have a testimony of the current one, does that mean the entire church is now wrong but led by a true prophet? No, that wouldn't make sense. Personally, I would Look at Joseph Smith Jr. and the current prophet before joining, and look at the others after joining. If you change your mind latter, you could always leave.

It boils down to a question of what do you think is the bigger sin, ignoring a prompting from the holy spirit, or following a prompting before studying it out? and I don't think I can answer that here.

EDIT So I was pointed to a Statement by a previous president, I would think this is a shortcut, gain a testimony of this and they you can not worry about the other prophets.

“The Lord will never permit me or any other man who stands as President of this Church to lead you astray. It is not in the programme. It is not in the mind of God. If I were to attempt that, the Lord would remove me out of my place” (Teachings of Presidents of the Church: Wilford Woodruff [2004], 199).

2.They do encourage this from what I understand. There is even a manual about this. It is an "institute" manual which I believe means it is a college level course. The introduction states:

The purpose of the Teachings of the Living Prophets Student Manual is to help you strengthen your testimony of living prophets and their teachings. It discusses our need for living prophets, the role of the President of the Church, the divine order of succession in the Presidency, the Quorum of the First Presidency and the Quorum of the Twelve Apostles, and the importance of general conferences. President Harold B. Lee (1899–1973) taught, “It is not alone sufficient for us as Latter-day Saints to follow our leaders and to accept their counsel, but we have the greater obligation to gain for ourselves the unshakable testimony of the divine appointment of these men and the witness that what they have told us is the will of our Heavenly Father” (in Conference Report, Oct. 1950, 130). A witness of the divine appointment of the living prophets is promised to each of us as we study the counsel of the Brethren and resolve to sustain them through our obedience. This manual will assist you in your study of the living prophets.

They also have a manual with the teachings from each prophet and it is another institute manual. Meaning, I think, They study all of them. They also have a larger book on each prophet (I think it's all of them), Scroll to the bottom of this page for the list of links.

3.From what I understand, they just ask you to pray about it and ask God. Seems pretty simple and straight forward. I would guess, that if the holy spirit already helped you out with a testimony of the current prophet, Joseph Smith Jr. and the Book of Mormon, this wouldn't be much more to ask.

EDIT After talking to a few more members I know, I was pointed to a "seminary" manual, which I believe is used with high school students. Page 158 of this manual. I would recommend you read the entire page about succession. The part below talks about the first conference that Brigham Young held:

“Brigham Young then spoke briefly, comforting the hearts of the Saints. As Brigham spoke, George Q. Cannon remembered, ‘it was the voice of Joseph himself,’ and ‘it seemed in the eyes of the people as if it were the very person of Joseph which stood before them.’ William C. Staines testified that Brigham Young spoke like the voice of the Prophet Joseph. ‘I thought it was he,’ Staines said, ‘and so did thousands who heard it.’ Wilford Woodruff also recalled that wonderful moment and wrote, ‘If I had not seen him with my own eyes, there is no one that could have convinced me that it was not Joseph Smith, and anyone can testify to this who was acquainted with these two men.’ [Quotations in History of the Church 7:236.] This miraculous manifestation, seen by many, made clear to the Saints that the Lord had chosen Brigham Young to succeed Joseph Smith as leader of the Church.

Answer 2

Short answer: They trust that God is in control and is ultimately responsible for ensuring that His prophet is in charge of the restored One True Church.

From http://www.lds.org/prophets-and-apostles/unto-all-the-world/prophets-of-the-restoration?lang=eng:

Since Heavenly Father and Jesus Christ ushered in the Restoration of the gospel and re-established the Church, the voice of the President of the Church has been a witness of divine, eternal truth.

Several LDS Scriptures support the idea as well, and are all listed at http://www.lds.org/scriptures/gs/prophet?lang=eng

A small sample:

• If there be a prophet, I the Lord will make myself known unto him in a vision, Num. 12:6
• I ordained thee a prophet unto the nations, Jer. 1:5, 7
• God hath set prophets in the Church, 1 Cor. 12:28 (Eph. 4:11).

In addition to the above, it may be that the definition of Prophet that you and I understand is not the same definition given in LDS theology. So, for the record, here it is:

A person who has been called by and speaks for God. As a messenger of God, a prophet receives commandments, prophecies, and revelations from God. His responsibility is to make known God’s will and true character to mankind and to show the meaning of his dealings with them. A prophet denounces sin and foretells its consequences. He is a preacher of righteousness. On occasion, prophets may be inspired to foretell the future for the benefit of mankind. His primary responsibility, however, is to bear witness of Christ. The President of The Church of Jesus Christ of Latter-day Saints is God’s prophet on earth today. Members of the First Presidency and the Twelve Apostles are sustained as prophets, seers, and revelators.

Answer 3

There is a rather important scripture from the Old Testament that @DavidStratton missed.

Amos 3:7 (KJV): Surly the Lord God will do nothing but He revealeth His secret unto His servants the prophets.

As the LDS church see's it, if the true chruch of Christ is on the earth, there Absolutely must be a prophet on the earth.

Now to answer your question: In the Doctrine and Covenants, the Lord laid out the foundation for how the church leadership was to be continued.

The person who has been in the Quorum of the Twelve Apostles the longest, is at the death of the old prophet sustained, and ordained the new prophet of the church. If you look at the history of the Quorum of the Twelve during Joseph Smiths day, Brigham Young was the senior apostle.

So for the general LDS population, everyone is instructed that they should come to their own belief in not just Joseph Smith but also the current prophet of the church. However if you have a testimony that Joseph Smith was a prophet and the revelation he received was from God, then it follows that as long as that revelation was followed each consecutive president would also be a prophet of God.

Little historical notes:

The history is a little messy because of the explosive growth of the church and the many people who either left/were excommunicated during that time. But he (Brigham Young) was the longest serving apostle and the president of the Quorum when Joseph passed away.

As a note of interest Hyrum would actually have been the next prophet if he had not died with his brother Joseph. However he was not the president of the Quorum of the Twelve because he was the 1st counselor in the 1st presidency of the church. And being the president of the Quorum of the Twelve even today is not necessarily an indication that you are the longest served apostle.

Answer 4

Interesting that no one has mentioned that the only person Joseph Smith favored to succeed him was his brother, Samuel, who died shortly after the martyrdom--probably murdered by Hosea Stout by poison, in an attempt to delay succession to the presidency until Brigham Young returned to Nauvoo from Boston. Both Samuel's daughter and brother William believed that Stout was acting under orders from Young and Willard Richards.

The enmity between Emma Smith and Brigham Young is well known, and Emma never recognized Young as the rightful successor to her husband. The real Emma is far from the Emma the Church portrays today, as is Brigham Young. I doubt many Latter-day Saints could gain much of a testimony is they were asked outright if they sustained Young as a true prophet of the Lord, or have even read the Journal of Discourses, and studied his heretical doctrines, such as of blood atonement.

Current LDS claims of succession are not based on any historical evidence, but only on the belief that the Twelve and not the Nauvoo High Council comprised the leadership of the Church. Even then, Young was not sustained as president and prophet until 1847, more than three years after the martyrdom. In other words, the LDS pioneers saw no need for succession or a prophet until they reached Utah.