I'd argue that the process you're talking about is more like the standard "uploading" process, minus the usual caveat about destroying the original. I agree with you that the process you describe process creates a copy that thinks it's the original. I also agree that destroying the original as part of the process seems arbitrary: why would copying someone's mind necessitate destroying the original?
But what I describe is a different process. Instead of copying the subject's mind into a machine, the user gradually learns to use the machine to supplement, or even outright replace, parts of his brain. There is only one mind, which works "across" both the brain and the machine simultaneously, rather than being cleanly "in" either location. Another poster mentions a prosthesis for specific brain functions; this is a good metaphor.
Transferring, then, becomes the process of working "across" both the brain and the machine, and increasing the machine usage to the point that the brain can be taken out of the loop. Assuming for the moment that this ever becomes possible, would that be a true transference, or still just a duplicate that thinks it's the original?