thinking back to the TNG episode where Barclay has a fear of the transporter, and subsequently finds people living in some kind of transporter limbo, He is conscious the whole time he is beaming in the matter stream. So this could mean that ones conscious being or "soul" moves with the matter. Or it means that transporters would need to be able to re-initiate life processes once the matter has been relocated. Otherwise a transporter would just take a live person in one place and make them into a dead person in another place.
My guess is when your body is broken down to the most simpliste state for transportation the molecules or even the atoms could carry what is known as your soul or the energy that defines you. Thats just what I think. I do believe in souls.
This question goes all the way back to the original series, and some of the first novels written for/about it. Just as the existence of souls is itself a matter of faith, not science, it can only be answered on those terms, and the answer is likely to be a personal one.
obviously cosciousness is a byproduct of our brians being configured the way they are seeing as how conciousness can be interputed or even removed all together by strokes and or brain trauma and leave use a veggie or even more or less brain dead if not brain dead.
So imho consiousness is somewhat linked to the idea of a soul but not entirely, and to state this I do believe in souls. I think it is much more likely that souls are both part of and seperate from you, more like an external harddrive, so when the primary eventually fails the external disconects and moves on with the total culmination of lifes experiences and in essence takes over where the body failed. And in the process of teleportation when one is atomized and reconfigured in the exact state it was dematerialized in the soul just follows the info to the new point and reintigrates, if it would ever not be integrated, cuz who is to say souls if they exist are not anywhere and everywhere at the same time, seeing as how the afterlife could work on completely diffrent physics if it worked on any kind at all.
If consciousness were merely a byproduct of our brain then there should be a way to measure it and master it. So far we haven't been able to and it's just something we can only talk about philosophically and literally EVERYTHING we know about it right now is based off assumptions. We assume everyone else has this sense of self. We assume you don't have it if you're a veggie. We assume you have the same sense of self if it goes away and comes back or we assume it's a different one.
We have theories and beliefs. No proofs. Heck, there's barely any evidence if any.
the transporter is just a fancy space fax machine, also in wrath of kahn kirk and marcus are carrying a conversation while in the materialization process. so it appears that you are totaly aware while you are in transit.