My take is that the only reason we have a feeling of a continuing thread of subjective consciousness is due to memory. The cells in our bodies are continuously being replaced, and there are breaks in our consciousness when we are asleep (or otherwise unconscious). So if a being has an identical brain structure to mine and identical memories, it IS me as much as I am. If you simultaneously delete me and create this copy, it's as much still 'me' as if I'd simply moved my body to a different location. The fact that it's comprised of different physical matter is irrelevant. It would have all of my abilities, thoughts, feelings, memories, and beliefs—it would be me. It would happily continue my subjective experience, relieved that the procedure to prolong life via this backup procedure apparently 'worked'.
If you created multiple copies, they would all be equally 'me', although obviously yes, as they then went on to live different lives, they would become different people from each other, just as there are many different paths my life could take looking into the future now.
If you created multiple copies, they would all be equally 'me', although obviously yes, as they then went on to live different lives, they would become different people from each other, just as there are many different paths my life could take looking into the future now.