Change is ssential to human nature. A human exists--and the same human exists--fron fertilization to death. Fertilization is a change before which we can say "not smeej" and after which, "smeej." And death is also a change before which we can say "smeej" and after which, "not smeej." There will be vastly, vastly more cells at death than there were at fertilization (assuming smeej made it out of the womb and to an observable state), and the original fertilized cell will no longer exist, but there is no other point along the existence of smeej in which a change happens of such significance as to alter whether or not the same thing is present.
The thing about a copy, it reproduces that pattern. The question is, how good does a copy need to be to retain the important features? For now, I suspect that any attempt to actually scan a brain would be a cargo-cult copy of a mind… but I don't know that for sure, I'm just going with what I hear from the occasional neuroscientist who bothers to comment on misconceptions in this field.