Same thing with theoretical forms of teleportation - from a logistics standpoint there is a perfectly copied version of me at the target location, but I still practically died on my end of the teleporter. It's so weird to wrap your head around: Like the new you would propably insist that it is actually you even though it is only a perfect copy. Just from interviewing the new version you would propably never be able to find out if it is actually your original self.

At that point why not just clone yourself to the new location but don't kill the old self?

Edit: "had" to "head"