This would be more akin to an afterlife rather than reincarnation. According to traditional reincarnation, your memories are lost. This leaves open the question of how the reincarnated person is still "you" but that's a standard problem with reincarnation theory. If one follows Buddhist reincarnation theory, the reincarnation results from the action of the prior incarnation (karma literally means 'action'). In that scenario, the lack of continuity would be a disqualifier.
Anyway, this idea has been discussed before. The question is, even if true, so what?
Anyway, this idea has been discussed before. The question is, even if true, so what?