Sorry about that ridiculous watermark.
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I think I’ve explained this too many times to do it again, but: teleportation doesn’t have to be “destroy and reconstitute” any more than going through a door necessitates killing you and reconstituting you on the other side of the door. The key is establishing continuity of your mind across the intervening space, which is mostly an engineering problem.
Star Trek transporters are “destroy and reconstitute” though. They are explicitly described as such. The whole Thomas Riker situation even requires it to be the case.