Can there be valid Apostolic Succession in multiple churches, such as Orthodox, Anglican, Church of the East, and Coptic Church? If so, how do Catholic church reconcile this with it's belief in being the only one true church?
Can There Be valid Apostolic Succession in multiple Churches?
The short answer is yes.
Apostolic Succession has been maintained in some Christian denominations such as within the Catholic Church, Eastern Orthodox Churches and Eastern Oriental Churches!
So what is Apostolic Succession?
The method by which the episcopacy has been derived from the Apostles to the present day. Succession means successive consecration by the laying on of hands, performing the functions of the Apostles, receiving their commission in a lineal sequence from the Apostles, succession in episcopal sees traced back to the Apostles, and successive communion with the apostolic See, i.e., the Bishop of Rome. The Eastern Orthodox and others share in the apostolic succession in having valid episcopal orders, although they are not in collegial union with the roman Catholic hierarchy.
In other words, apostolic succession, in Christendom, is the teaching that bishops represent a direct, uninterrupted line of continuity from the first Apostles of Jesus Christ. According to this teaching, bishops possess certain special powers handed down to them from the Apostles; these consist primarily of the right to confirm church members, to ordain priests, to consecrate other bishops, and to rule over the clergy and church members in their diocese (an area made up of several congregations).
Thus the Catholic Church, the Eastern Orthodox Churches and the Oriental Churches all have valid Apostolic Succession. Rome recognizes that the Eastern Orthodox Churches and the Eastern Oriental Churches have valid episcopal authority and valid sacraments.
The Anglican Church does not have a valid episcopal succession according to the Catholic Church. In 1896, Pope Leo XIII affirmed in his 1896 encyclical Apostolicæ Curæ (On the Nullity of Anglican Orders), neither does apostolic Succession exist within the Anglican hierarchy.
Although some Churches may have Apostolic Succession, in Rome’s eyes the situation is a little more complex.
Roman Catholics recognize the validity of the apostolic successions of the bishops, and therefore the rest of the clergy, of the Eastern Orthodox, Oriental Orthodox, Church of the East, and Polish National Catholic Church. The Orthodox generally recognize Roman Catholic clerical orders as being of apostolic lineage, but have a different concept of the apostolic succession as it exists outside the canonical borders of the Eastern Orthodox Church, extending the term only to bishops who have maintained communion, received ordination from a line of apostolic bishops, and preserved the catholic faith once delivered through the apostles and handed down as holy tradition. The lack of apostolic succession through bishops is the primary basis on which Protestant denominations (barring some like Anglicans and Old Catholics) are not called churches, in the proper sense, by the Orthodox and Roman Catholic churches, the latter referring to them as "ecclesial communities" in the official documents of the Second Vatican Council. - Apostolic Succession
The authors of the Catholic Encyclopedia state that the Catholic Church alone can validly claim Apostolic Succession, but this is incongruent with genuine Catholic thought, as some Eastern Churches have valid clerical orders and episcopate and are deemed valid, thus their Apostolic Succession is quite valid. Without a valid episcopacy or Apostolic Succession, there would be no existence of ordained clergy! The authors of New Advent are simply expressing their personal opinions in this matter. I have notice other errors in their works, although few are still there.
They claim that only the Catholic Church has a valid claim to Apostolic Succession because others are outside the unity of Holy Mother Church. This is in fact not true. Their Apostolic Succession is valid and is quite well recognized as such by Rome.
Apostolic succession depends upon the validity of episcopal consecration.
Anglicans do not have valid Orders, as Pope Leo XIII affirmed in his 1896 encyclical Apostolicæ Curæ, so neither do they have valid apostolic succession:
[…] when in England, shortly after it was rent from the center of Christian Unity, a new rite for conferring Holy Orders was publicly introduced under Edward VI, the true Sacrament of Order as instituted by Christ lapsed, and with it the hierarchical succession. […]
[…] we pronounce and declare that ordinations carried out according to the Anglican rite have been, and are, absolutely null and utterly void.
The schismatic Easterners use a valid rite of episcopal consecration, so apostolic succession can continue with them.
It appears there is some confusion about what "apostolic succession" actually means.
According to the 1907 Catholic Encyclopedia article Apostolic Succession, Rome alone has apostolic succession:
Apostolicity as a note of the true Church being dealt with elsewhere, the object of the present article is to show:
- That Apostolic succession is found in the Catholic Church.
- That none of the separate Churches have any valid claim to it.
- That the Anglican Church, in particular, has broken away from Apostolic unity.
The principle underlying the Roman claim is contained in the idea of succession. "To succeed" is to be the successor of, especially to be the heir of, or to occupy an official position just after, as Victoria succeeded William IV. Now the Roman Pontiffs come immediately after, occupy the position, and perform the functions of St. Peter; they are, therefore, his successors.
In particular, it makes clear that none of the Eastern Churches have a valid claim as long as they remain apart from Rome.
The Greek Church, embracing all the Eastern Churches involved in the schism of Photius and Michael Caerularius, and the Russian Church can lay no claim to Apostolic succession either direct or indirect, i.e. through Rome, because they are, by their own fact and will, separated from the Roman Communion. [ibid]
So, to answer the OP, no, from the point of view of the (Roman) Catholic Church.
TO ADD ON MY FIRST SENTENCE. The confusion is some believe "apostolic succession" simply means an unbroken line of bishops back to an apostle. All apostles taught the same faith, thus, any church with an unbroken line has apostolic succession. This is so regardless of what they might teach. The filioque is a prime example. Both Eastern Orthodox and Roman Catholic believe themselves and the other to have apostolic succession, even though they do not teach the same.
Quote from the Catholic Catechism paragraph 1399:
"These [Orthodox] Churches, although separated from us, yet possess true sacraments, above all - by apostolic succession - the priesthood and the Eucharist, whereby they are still joined to us in closest intimacy." A certain communion in sacris, and so in the Eucharist, "given suitable circumstances and the approval of Church authority, is not merely possible but is encouraged."
In short, apostolic succession may be defined in three ways. One, you have apostolic succession if you teach the same as apostles (think Reformation). Two, you have apostolic succession if you have a lineage from the current bishop back to an apostle, regardless of what you teach (think filioque). Three, you have apostolic succession if you teach a sacerdotal communion (think Catholic, Orthodox, but not Anglican; per CCC 1399.