I don't think that consciousness has momentum.
You're really talking about (at best) a new instantiation of the identical consciousness in a new body. That's not the original consciousness moving, that's a new (identical) consciousness coming to life.
I am unconvinced a consciousness can migrate out of the body that it's in. Copies are not enough.
This is made more obvious if you consider the case that the original is not destroyed. Then the clone that comes out of the end of the transporter would be having experiences that the original can not experience. If they were really one consciousness they would have one experience from that point on, but they don't. They're two different people.
So in the first case one person dies and another person with the same body and memories is born, and in the second case the first person does not die and another person with the same body and memories is born. In both cases they are two separate people.
This is making a lot of assumptions about how consciousness works. If I make a copy of a book the story doesn't move, but it is now in two places. If I destroy the original book the story isn't lost. I think experience might be more like that. Multiple copies of the same information system will all only have one subjective experience.
Yes if you run two versions they will diverge and the question is much more complicated. But if there is one moment of copy/destruction or you're scanning and then simulating/rebuilding a frozen brain, then there's no point in time where a consciousness doesn't have a future version.
There's a mechanistic, reductionist point of view that runs throughout many of the HN comments here that I find really disturbing.
A lot of people seem to think that we are just machines. If we are, then sure, replacing one machine with another that works the same and has the same "data" might be unproblematic, but I don't share such a bleak and narrow view of humanity. To think and feel is not just to run a program on a computer.
I don't think it's less mechanistic to say that the second copy creates a second entity.
Why do you think that the thinking and feeling is tied to the original body?