Suppose we are living in a time when medicine has advanced tons. In this time, a friend of yours gets into an accident, and gradually starts to lose different body functions/parts. Each time a body part stops working, it is replaced with an artificial one. There comes a time when everything physical about your friend is replaced, even his brain. Though during brain change (say brain is replaced with a chip), all his memories are shifted from his old brain to the replacement. When this physically totally new friend of yours wakes up after the memory transfer, he claims he is your friend, and can answer any question you throw at him, that would have been answered by your original friend.
Is this physically new friend actually your old friend? Or is he faking it having access to all the memories of your friend? Did a "consciousness transfer" occur as well? Or not?
Any take?