I submit that in the atheist worldview, this is not a logical problem, and in the Christian worldview it is a huge wrench in the spokes. For example, that person would demonstrably have consciousness, and would likely have a belief system of some sort, even if it differed from the original person's. Thus arises the question of what happens if they become Christian and a genuine believer. (I don't see any reason why this can't be the case.)
I'm not meaning to discuss whether or not it is moral to clone a person (and my personal belief on this is that we should never, ever do it.)