Hans Moravec wrote a book, _Mind Children_, in which he provided a thought experiment where consciousness could be transfered even by the standards of a process

Hans Moravec wrote a book, _Mind Children_, in which he provided a thought experiment where consciousness could be transfered even by the standards of a process-partisan (as opposed to pattern partisans, for whom every sufficiently like mind is really them). The idea is to do the transfer in real time, building a copy of a tiny portion of the brain, then running the copy-portion in parallel with the original-portion until it's producing the same output given the same input. At that point, you can reroute control through the copy (running at the same speed as the rest of your brain), and remove the brain matter that was copied. If you do this to pieces small enough that the loss of each piece would still leave you essentially you, the whole procedure can smoothly transfer your consciousness into a brain simulation while you're awake and feeling like yourself.