If you were to be duplicated just before you died and the duplicate survived, would it be you?
This can be seen as a deep philosophical question with a myriad differently nuanced answers. But I'm not much of a philosopher so my answer is simply "no". A duplicate of your entire person or a perfect molecular copy of your brain, could be just like you for some period time but it would not be you.
The soul-mongers may be rubbing their hands with glee at this point but this has nothing to do with them or their fantastical constructs. Their agenda is to promote the notion of a unique ethereal part that "lives on" somehow after you die. By their definition the duplicate person would have no soul - one person one soul - that's all that God hands out (then takes back). What a quaint and morbid idea.
We cannot make such a copy at present so you can think of this as a thought experiment. In the relatively near future we will be able to make such copies and there will be various ways of doing this. The copying will not be the problem, the method of the state/substrate transfer process may be.
Let's say that the scientists doing the copying decide to conceal who is the "original" and whom the "duplicate", even from themselves. Immediately after completion of the copy process both entities would insist that they are the "real" version of the person and both would be correct. If you dispute this then, in what sense would they not both be correct? Let's not get hung up on which of them would be composed of the most recently rearranged atomic material. But that is all it really comes down to. Then divergence sets in.
When does the divergence between the two entities set in? How much do they diverge? Pretty much immediately or somewhat later. A little or vastly. What does it matter? They diverge, they are not the same person. This could be an excellent moral thought experiment for the religious if they were a little more imaginative - they could have a 'soul dilution' construct with each duplicate being, in comparison to the pre-duplication 'original', a kind of watery orange squash in the soul department.
There is, of course, no dilution. Both versions are valid entities ready to go back out into the cosmos on their own divergent paths, no matter how closely they stick together. But weren't we talking about the death of the "original"? This kind of duplication wouldn't save you, so what would? Well, we know that we are constantly in the process of being rebuilt at the molecular level and that, every few years, every atom in our bodies will have been replaced. So in what sense are we the "same person" as a few years previously? The key is that we feel the same because of our memories and the continuous "psychological flow" of our being. When we think back we don't usually detect vast gaps prior to which we suspect that we may have been somebody else. The psychological continuity of the self is an illusion but a very useful one, and one that we feel we must maintain in order for "me" to mean anything. So if there is to be any kind of 'movement' of our 'selves' from one state/substrate to another there must be a transition process which maintains psychological continuity.
I have imagined that this could be done with a future perfected version of a virtual brain akin to the Blue Brain project. A perfect human/virtual brain interface would also be required. The neocortical columns of the dying person are wired to the virtual brain and data communication begins at whatever level of resolution/fidelity is required. At first the 'generic' virtual brain is acting only as a relay so that the patient's columns can adjust to the new environment. Gradually some of the less-active columns in the bio brain could begin to 'share' some thought/memory structures with the virtual, allowing the virtual brain to 'learn' the bio brain's structure and patterns. The virtual columns gradually take on more and more responsibility until the virtual brain is handling entire neocortical areas, and the virtual and bio are operating as one entity. The process continues until only some autonomic functions, such as regulation of blood oxygenation, are being handled by the bio brain. The virtual brain does not strictly require autonomic functions but some simulation of those functions would be required in order to prevent the patient from suffering a kind of ontological shock brought on by the realisation of the substrate transfer. If required the biological body and brain stem can continue to function in tandem with the virtual brain indefinitely but the transfer of the 'self' to the new substrate is now complete.
I don't think it's looking good for teleportation. A teleport would be a kind of duplicator/destroyer device. Let the duplicates live. Anything else would be unthinkable. But this isn't about duplication, it's about transfer. And here's where it does get philosophical. Have you ever felt like you have, even for a short while, become "one" with another person? It can be joyful, unsettling or both. I think it's a realisation that our boundaries are mutable and that we could, ultimately, accept a new substrate as home.