I'm not convinced there's any such thing as a self, let alone a soul.
What I might refer to as "me" is an aggregate collection of tenuously connected or related thoughts, actions, preferences, points of view, perspectives, physical traits, memories, knowledge, and opinions. That collection is constantly changing, with bits being added and subtracted from it every second. The person I am today has had different experiences than the person I was a week ago, and depending on what's happened during that week, I may have very different opinions, knowledge, or beliefs about certain key issues. The person I was just ten years ago may not even resemble the person I am today, in terms of personality, education, or point of view.
However, despite the idea that there can never be a persistent state of being that we can pin down as being a given person's "self," our understanding of living creatures and of the mind absolutely depends on pretending like there really is one. At best, we can say that while any part can be taken from or added to the whole, it's the "arrangement" that constitutes the "self." To me, this is horribly vague, and brings up more questions than answers.
The claim of a "soul" is a way to smear over this whole problem. It posits that there is this magical thing which really is you in some way, without ever really demonstrating how that is. To me, someone who says that the "self" is contained in the soul is someone who doesn't understand the issues at hand.
But, back to the original topic: yeah, claiming that some kind of teleportation or reproduction experiment proves the existence of a soul is a non-sequitur if ever there was one.
I'm not sure where I stand on where "you" are, though. It would depend on the circumstances. If you really could perfectly (and I mean, perfectly) replicate an entire person and make a copy that has all the same memories, thoughts, and experiences as the original -- then there might be some infinitesimal instant in which the difference between them could be negligible, or non-existent. But, even that is doubtful, since those two beings would have to inhabit the same space. And, as soon as the two begin having experiences separate from each other, they are different people from each other. The observation that the two are extremely similar, and the fact that both share the same memories, is a red herring. In reality, only one of them actually existed before the replication.