Spend some time testing this on stream the other day.
Results:
You have to create your own runewords to get completion.
You have to be in the game when the item drops.
You and all players still have to be in a game to get completion upon identifying the item(s)
You can still bring the item(s) to a new game and identify with the same players (Not character based, but account based)
So you cannot trade your way to completion, and you cannot join a game where the item has already dropped.
Thanks. I did have some instances whereby an item doesn't count after leaving the game, if stored in stash I think. Did you manage to test this or experienced this yourself?
How about someone unparties/hostiles within the same game, do they still share the completion?