I'm sure it's been discussed before, but I must have missed it.
All of the other Assassin's Creeds always had an explanation of why you could continue to use the Animus after the end of the game. However, with Desmond dead (presumably), there really only leaves three explanations as to how you can continue to control Connor after the end of the game:
Desmond is not really dead Desmond is no longer the one controlling Connor Developer oversight
Considering the epilogue dialogue (lol) concerning the Animus hacks and synchronizing to the Cloud, I'm pretty confidently going to say it's not the last one. So, let's discuss. Do you think Desmond is not really dead (this means alive in ANY way, shape, or form), or do you think Desmond is no longer the one in control of Connor during the epilogue sequences? If so, who do you think you are playing as during the epilogue?
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I think it's pretty obvious Desmond isn't in control. Whoever is hacking the Animus is either a relative of Desmond and Connor, or now with enough hacking points anyone can relive memories from an Animus.