Exactly my point. Either there is a ‘soul’, or man is just a machine, and our conscious minds nothing more than a very complex analog computer.
If that is the case (and I believe it is), then that doesn’t slam to the door on immortality. All we need to do is recreate my brain some time in the future, and I’ll ‘wake up’.
Sounds like Star Trek to me. Unfortunately, that’s no less a fairy tale than resurrection. For a teleporter to recreate your brain, it would have to record the quantum state of each atom and recreate each of them simultaneously in precisely that state. One of the fundamental claims of Quantum Theory is that such measurements cannot be performed without disturbing the object being measured.
A different type of immortality is feasible, if space-time actually exists as a four-dimensional manifold embedded in a higher dimensional manifold with its own independent time axis. From the perspective of the containing manifold, all points in our timeline might be observable simultaneously. In effect, our entire lifespan would be “frozen in time”, as if each moment in our lives had been captured on a hyper-dimensional videotape.
But Heisenberg compensators will dispel that myth. 
What makes you think the mind runs at that level of resolution ? The brain is full of noise and messyness; I doubt it would matter if a duplicator/transporter only gets close to the original, as long as it’s close enough.
That’s an “immortality by philosophy”, it’s not what most mean when they use they word.