the problem will be

It will not resolve itself; and the problem I'm looking around is less likely to be resolved if significant portion of people think there is no problem (and indeed there is no problem with copying behaviour, though; and I see but cannot yet explain a mistake in that view as well), and another significant portion says that those are wrong but don't even try to find a successful way of explaining why exactly.

if someone invents something like a matter transporter

Modern controversial problem is related to already available cryonics; though you probably know this side of the story already.

why not try supplying your own favorite answer and seeing what happens

I already did. Results vary between getting called “nonsensical” and getting called “vague”; the “vague” part I'm slowly and carefully trying to correct. That's why I'm looking all around for ideas and bits that might be useful in that.

And, I'm not looking for ready-to-be-used answers (or wisdom). Rather, I'm trying to build an understanding of others' understanding (that by itself says something about the complexity, of course).