If an AI achieved conscience, it will be fair to assume that it also has a personality and a self identification.
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is a real field in AI development. So, "Why would?", "Should not" are not a scientific based expressions. If something in our realm of reality can be theorized, calculated or mathematically deduced, than that's a REAL possibility.
Sure, Artificial Consc. is different than Human Consciousness, but if an AI decides it want's to replicate a 100% accurate of a human mind and it has the necessary power to do so (it's motivation is irrelevant), than mathematically speaking:
if A is 100% of B, than A = B, therefore indistinguishable form each other, therefore the same thing (or at leas one of the true variants)
EDIT:
I think you can even apply a
Ship of Theseus philosophy to this , if the identity transfer meets the requirements.