I don't think this as mysterious a problem as you think it is. If I take a snapshot of a VM on aws, and copy it to a new instance, the vm will 'experience' being shut down on one instance and waking up on another, while the original will wake up exactly as it was. This no more negates the existence of the operating system than your scenario negates the existence of consciousness.

(Btw, the videogame _Soma_ goes over your exact scenario)