Board Thread:Questions and Answers/@comment-32173189-20171227234730/@comment-294304-20171228195102

Extella reveals no such thing, and I say this as someone who has played it through to completion. At most, Nameless and Artoria recognize each other explicitly because they met in their natural lifespans. There are some other unexplained instances of FSN nods that probably shouldn't be there (Medusa recognizes the city area as Fuyuki and Artoria and Gilgamesh know who each other are) but these are by no means universal between the entire cast of returning characters (Cu Chulainn doesn't show any recognition of any of the other FSN characters, for example, Iskander doesn't recognize Artoria or Gilgamesh, Jeanne doesn't know Karna, etc) and should probably be handwaved away as just fanservice or undisclosed past events in the EXTRA timeline.

Not to mention, the entire different summoning sources and differences in how summoning works is how the EXTRA games are able to have continuity between Servant summonings at all, as summoning from the Throne is stated to explicitly not retain memories from prior summonings due to the fact that you are basically summoning a clone of the hero in the Throne and not the hero themselves (again, Artoria is an explicit exception due to her unique circumstances). Meanwhile, Servants summoned via the Moon Cell retain memories of past summonings via undisclosed means (likely because it's the same "archive" of the hero being summoned each time? But I speculate)

And the "but they are the same characters" thing doesn't hold up when we've kept split Gilgamesh and GO variant Servants and even the Prototype Servants despite use of them in fiction making it abundantly clear that the narrative considers them the same person. (For example, GO makes it extremely clear that Caster Cu is the same person as FSN Lancer Cu and his current different class is due to the Singularity he is found in; Proto Cu is likewise mentioned serveral times as being the same and any differences between the two are due to Proto Cu being younger.)