if we adopt idea that consciousness could be different without any physical difference between the copies, we adopt the idea of p-zombies and reject physicalism that is modern version of materialism. It almost the same as to say that immaterial soul exist. It is very strong statement.

Not relevant to the problem. If you create a copy of me, the copy is not identical, if for no other reason than it occupies a different location than I do. I agree that if it occupied the same location that I do, atom for atom and quark for quark, that could lead to the concern you express. But copies cannot occupy the same location, and so there is no problem having the copy to the left be one consciousness while the original to the right is a different consciousness.

The strongest claim I might accept would be that both the original and the copy have "valid" claims to be the continuation of the pre-copying single consciousness that was me back then. But no matter how you slice it, killing the original when you make the copy is still destroying a separate consciousness, even if the remaining consciousness thinks it is the only continuation of the pre-copy consciousness.