This is the Star Trek transporter conundrum. When the transporter rips apart every atom and quantum state in a person’s body during scanning and then creates a copy out of energy at a distant location, is the transported person the same? Are they killing a person each time they’re transported? Kirk, Spock and Scott don’t seem worried, but Bones is never comfortable with transporters.
I think the answer is, 'We don’t know they’re the ‘same’ people". But then, we don’t know if we’re actually the same thing day to day. We have the feeling of continuity but is it real or just a memory of past states?
I tend to favor physicality, that what we perceive as consciousness is the result of patterns and processes. If you’d freeze the process and duplicate conditions exactly in another substrate, you’d have effectively the same going forward. With duplication, you’d initially have two of the same before later events & experiences produce divergence. Whether the consciousness that is reproduced is the same ‘metaphysically’ is not something I think we can resolve. Best we can do is ‘try it and see’.
On a somewhat related line, we can ask the same of what happens with identical twins. In that case we have two clones split off the same individual egg. If a ‘soul’ is related in some way to the continuation of consciousness, then was one soul divided into two? We assume each twin has a distinct soul/ ‘kernel of consciousness’. Or is one a zombie-brain?
There is another science fiction series related to the notion of indivisible, unreplicable (is that a word?) souls. In that story, ‘souls’ can be induced to enter a body that is sufficiently similar to the body it used to inhabit. People can be resurrected ‘totally’ in this story and souls can only bind to one body at a time. Cloned bodies remain unconscious until an ensouled body dies and the initial connection releases the soul to bind to a new body (“To Your Scattered Bodies Go”, by Philip José Farmer).