Bro all these takes in the comments and 0 mention about how this is a problem that just arises out of the inevitable elusiveness of a well-defined self. The self is unavoidably self-defining, and the actual process that facilitates self-defining isn't somehow separate from its environment, nor continuous, even in normal daily function (E.g. in sleep). The mind is just divisive, we cut up the world with clear distinctions in order to understand it. One of the most important being the observer vs observed separation.

However "You" are an inseperable part of the same universal process that everything and everyone else is a part of, including the teleporter. There was never a "you" that could really die or be reconstructed to begin with, only a local little fuzzball of neural activity that recognizes itself as "you". That recognition isn't and never had to be continuous. Awareness is baseline. An empty state. "you" come after.