So there's certainly an argument to be made that if someone created a copy of "you" and put it in a robot, and then destroyed your organic body, that consciousness wouldn't "move" to the robot; it would stay in the organic body and be killed. The robot would be a completely new consciousness, but with all of your memories and behaviors and attitudes.
I'm honestly not sure what I believe around this. Perhaps we will discover "consciousness" as a physical thing and learn how to transfer that as well. Or not. Who knows.
That said, I wonder if that offers a possible way to 'transfer consciousness' between a human and their robot copy - link both brains together and then once synchronised (whatever that means), shutdown the biological half. Like a sort of extended Ship of Theseus idea.