I don't know anything about the brain but if it was reconstructed exactly how it was before being teleported, wouldn't it possess the same memories, knowledge and thoughts..?
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Yes. So what if you had a clone that just THOUGHT it was you? I mean your originally got disintegrated and killed man. Then reconstructed. So your clone would think it's you, everybody would think it's you, but of course nobody would know that you are dead and this doppelgänger has taken your place.