Precisely my problem with it. Surely you’d have to be taken as a whole, otherwise your entire conscious state would be lost ( for however brief a period it may be ) between these theoretical teleporters.
Would the person that came out the other side though not think he was you? His brain would be made up the exact same way, so assuming memories are hard wired into our brain, he would for all intents and purposes believe he is you.
However he would be an entirely new entity and you would of ceased to be the moment your atoms were broken down for transportation.
I think I’d much prefer to go by wormhole myself.
Less of that “will I actually exist on the other side” worry.
It would be interesting to see the problems associated philosophically with the importance of self if we could literally break someone down and rebuild them without a care for the original.