Was the Synagogue of Satan the same as the Synagogue of Libertines?

Question

If the Synagogue of Libertines (Acts 6: 9) was Hellenist it would not have been regarded as properly Jewish by conservative Jews.

Then there arose certain of the synagogue, which is called the synagogue of the Libertines, and Cyrenians, and Alexandrians, and of them of Cilicia and of Asia, disputing with Stephen. (Acts 6:9, KJV)

Is this what Revelation 2:9 and Rev. 3: 9 talks about?

I know thy works, and tribulation, and poverty, (but thou art rich) and I know the blasphemy of them which say they are Jews, and are not, but are the synagogue of Satan. (Revelation 2:9, KJV)

Behold, I will make them of the synagogue of Satan, which say they are Jews, and are not, but do lie; behold, I will make them to come and worship before thy feet, and to know that I have loved thee. (Revelation 3:9, KJV)

Answer 1

Most synagogues outside of Israel would be influenced by Greek culture and therefore of the 'hellenistic' variety, so the Libertines, Cyrenians, and Alexandrians, and of them of Cilicia and of Asia, were probably among them. What conservative Jews may or may not have thought about their brethren would have no bearing in what they thought about themselves. Probably both conservative and Hellenistic Jews would have considered Christian Jews as not Jews at all and Christians at large as not God's children. Therefore when we come to Revelation and find Jews claiming the title of 'Jew' while denying the title to Christians, who were true Jews in spirit, in Symrna (a city near Ephesus) they would be a very similar synagogue like those in Acts. However they would not be the exact same synagogue but probably one assembling right in Smyrna, at tongue lashing distance of that church who suffered under their slander directly.

Answer 2

"Synagogue of Satan", according to theologians, may refer to -

1. Assembly of Jews who rejected Jesus Christ and persecuted the Christians

   (Pulpit Commentary)

   We have here strong evidence of the early date of the Apocalypse. Throughout this book "Jew" is an honourable name for the worshippers of the Christ; "Gentiles," a name of reproach for those who oppose the Christ. [...] These persecutors of the Church of Smyrna are Jews in name, but in reality are rather Gentiles - opponents, and not worshippers of the Messiah. (source: Bible commentaries on Rev 2:9)

2. Heretics who professed Christianity

   (Gill's Exposition of the Entire Bible)

   they professed Christianity in words, but in works denied it; they were men of bad principles and practices, and both blasphemed the ways and doctrines of Christ themselves, and caused them to be blasphemed by others also; they were false Christians, nominal professors, and shunned persecution for the Gospel; who were not what they would be thought to be: these were the broachers of heresies in this period of time (source: Bible commentaries on Rev 2:9)

"Synagogue of Libertines" was probably the assembly of the Freedmen from Rome, descendants of the Jews enslaved by Pompey after his conquest of Judaea in 63 BC. (source). They were persecuting the Christians, they were responsible for the death of Stephen, the first martyr.

Synagogue of Libertines were Hellenistic Jews and were persecuting Christians. If "Synagogue of Satan" means "Jews who reject Christ", then we can deduce that "Synagogue of Libertines" was indeed one of the Synagogues of Satan mentioned in Rev. 2: 9 and Rev. 3: 9.