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.