I've never heard of any jew who believed in reincarnation. I call shenanigans on this story...it smells of a practical joke.
What? You haven't heard of the more mythical nature of Judiasm like the Golem or dybbuks? In this case, the implication is more like "possession" than "reincarnation".
You should watch A Serious Man --first it's a really good movie by the Coen Bros, second it opens with a scene based on the supernatural concepts of Jewish mythology before going into a more traditional tale set in the 60s.
Here's the scene:
(it's an awesome movie btw, it's the most spiritually agnostic film I've seen)