Not to mention the question how to define 'me' when two information systems (brains) both claim to be thesame 'me'. The continuation of ones awareness is the question here.
I just want to say something to this question. I pass on the rest

Imho, two distinct information systems, in this case brains, cannot claim to be the same 'me'. They are distinct systems and therefore are distinct 'me's'. What they CAN claim is the discriptions to be the same. Two brains can both call themselves Barney, be 28y 185d 5h 34m 6sec old, have a wife and two children, work as professional nonworker and so on. But they'll never be the same 'me'.
So if you "copy" ones 'me' (assuming this could be possible) would create an new 'me' and keep the old. In the very moment you pack the information of one system (the one whose awareness continues, as you claimed) into a second system, you created a second 'me' with distinct perceptions, after years perhaps with distinct believes and desires.
Have you seen the movie,where Arnold Schwarzenegger was cloned and wanted his life back, which was taken by the clone (or the other way round

)? This gives you an idea of what I mean.