It was while I was a student that a story hit the headlines about a 14 year old girl living somewhere in England who could remember a previous incarnation as a novitiate in a French convent some hundreds of years ago. The proof was that she could speak medieval French despite never having had any contact during her current lifetime with the country or its language
Assuming she really could speak Medieval French (how would they know?) I wondered if there could be a rational scientific explanation
Well, if memory is somehow encoded or recorded in molecules (I use that term loosely) in the brain then when the body finally decays those molecules will be released into the world. And since the amount of matter is fixed those molecules will over time quite likely form part of other human bodies. One day the molecule could end up in precisely that bit of someones brain which has the software & connections needed to decode the information
QED
Related post: The Ilkley Moor Argument