I was reading the Wikipedia article on reincarnation (and other research) to see about this, and apparently Indian religions didn’t introduce art-of-moi’s type of reincarnation until recently. So it could be a Jewish idea first that they appropriated from us.
I did crack up, however, when there was a picture of a Jainist reincarnation symbol on the page. It was a Hamsa. So much for those who thought that a Hamsa was a Jewish mystical symbol…