There you go. The point is not that the mid or personality is or is not duplicated and possibly identical (this depends on your definition of continuous identity) - rather, the point is that the computer to which the program is transferred is not the same as the first computer. You said yourself "another suitable brain;" this means you accede that it is not the same as the first brain.Perhaps an acceptable analagy would be a computer program. The program can be shut down, transfered to another computer,... Since a mind works by electricle impulses it isn't unreasonable to assume that it could be transfered to another suitable brain or possibly duplicated.
Seafort and I agree that the initial body is destroyed and that a qualitatively identical consciousness is created in a simulacrum; we differ in whether or not that is enough to presume continuous identity. I have delineated my own personality theory of personal identity earlier in this thread, q.v., while Seafort believes that physical identity is also necessary for personal identity; however, neither of us would say that there is a third possible criteria in the form of some nebulous and dubious "soul" as separate from both the physical body and the cognitive function. Such an assumption violates both Occam's Razor, and entwines the debate with religions - some of which come down on either side of the idea of the soul being either qualitatively or numerically identical, and so provide no assistance to this discussion at all.