I've been thinking more about this...
How can the Orthodox claim to have unbroken succession in regards to the Patriarchates of Antioch and Alexandria? The original holders to them are the Syriac and Coptic Orthodox Churches, respectively.
Is it possible that both can claim unbroken succession? I don't know the history of the Patriarchates well enough to say for sure, but it's a possibility.
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In today's world, both patriarchates treat each other as if they were two bishops of different dioceses in the same geographical area, specifically in Alexandria and Antioch where inter-communion has now been encouraged.
Just a nice piece of trivia: Our pope in history, Pope Cyril the fifth (I believe, not sure) was actually trusted to take care of the Greek Church in Alexandria while the Greek Pope of Alexandria was out to a council with other bishops and patriarchs. There were times of warm friendly love. It was also rumored a unity in Alexandria was going to happen at the time, but the Greek Pope was killed by the Muslims before that happened. We also have maybe one or two Chalcedonian Alexandrian Popes revered as saints in the Coptic Church.
So there were times of division and hatred and times of love and unity. The latter seems to dominate today.
Can both claim unbroken successorships? Yes, and they actually have a list. The real question probably is can both lines be valid? It seems like the question is yes according to today's ecumenical practices, unless you happen to disagree.
Also, to answer the reason of intercommunion, for the EO's and OO's, if intercommunion is encouraged, it is for the reason of being convinced of a united faith more than for pastoral reasons. With Catholics, there isn't a united faith to establish such reasons, so if there is intercommunion, it's for whatever pastoral reason given. We Copts generally frown on any communion with a Church that does not have the same faith. That's why it's acceptable with EO's, but not with any other Church. The Ethiopians, Eritreans, and I believe the Independant Indian Orthodox believe the same way too (in fact, I've heard many Indian Orthodox use Syrian intercommunion with Catholics as a polemic against them).