I believe this thought experiment raises the following question : is one consciousness (sentience) unique ?

One answer could be that there can't be two identical consciousnesses, ie if you have two identical clones experimenting the exact same life, then they share only one sentience. If there were more than one, they would be different in some way. If consciousness is what is, in some way, computed by their brains, then this output can be produced in different brains, but it only exists once. It is quite similar to the "conceptual differenciation" proof for the unicity of god.

In this case, the one who wakes up after I went to sleep or taken the teleporter is still me, since the brain hasn't changed significatively. Weirder is the fact that your consciousness may not be dependent on time itself : if someone has built a brain in the 19th century that is identical to yours the moment you die, maybe you would just "wake up" there.

And falling asleep wouldn't be so frightening (SMBC is a great web-comic I recommend).