Keep your brain in one piece
Good advice.
I think I can answer this:
it seems that the Star Trek transporter concept does not actually destroy something and rebuild a new copy, but actually just disassembles the molecules and pipes them to a new location for reassembly.
Which only means that the transporter sends along raw materials from which the destination object is (re)constructed. The outcome would be no different if local raw materials were used. It's not necessary for the same atoms to be present in the neurons, only that the neurons be assembled into the same structures as the original. Structure is everything, and precious in an entropic universe. Atoms are a dime a dozen.