Do they have precisely the same memories, neural structures, implicit skills, and characteristics, down to a resolution that is not distinguishable from the moment-to-moment procession of consciousness in the brain? Is their brainstate at time = T identical to that which would have proceeded from one of the original's brainstates, and does it proceed to develop in the same way, thereby rendering it causally connected?
Then yeah, miraculously, you've been resurrected. It seems crazy, but it's exactly the same as if you rot for a billion years and then some kind of crazy Anti-Entropic Field pulls you back together exactly as you were. Or if you're dead for a year, and your body is partially reconstructed by nanomachines - same principle. It's different matter but the same pattern. Basically, you've been teleported.
Bear in mind that the probability of this event occurring is staggeringly low. You're presuming that this duplicate has received precisely the same sensory input and physical stimuli. This means that everyone around them, all the weather, all the politics, all the everything has to be the same - the same stars in the sky, the same cosmic background radiation sleeting random particles into the brain. In fact, the only way for it to have happened is for them to have lived exactly the same life you did in exactly the same environment.
Of course, in a spatially infinite universe with regular matter density, the occurrence of such an event is actually inevitable, and you can actually calculate the average distance to an identical copy of you in existence right now.
tl;dr version: if you were teleported, and all the cast-off atoms of your existence formed a dead duplicate of you in the ground, you'd still consider yourself alive and the same person. It's the same scenario.