They feel like a "you", but many of those who go through amputation surgery do, indeed, experience "phantom limbs" and experience a deep sense of loss for long

They feel like a "you", but many of those who go through amputation surgery do, indeed, experience "phantom limbs" and experience a deep sense of loss for long periods of time after the surgery. In contrast, animals don't seem to go through the same "mourning" process (in a way that we would recognize). So the sense of "you" persists, yes, but it's a foundational change to the sense of "self" and it's definitely affected by amputation.