Without an enduring quid between lifes, how to explain past life recalling? How a being (be it a Buddha) can remember its past lives, if there is no "quid"/soul/self enduring for more time?
A self wouldn't help in this case; a self is an untenable entity - it is permanent yet able to change to know multiple objects, an illogical paradox.

The very idea that a memory can be stored isn't tenable, because memories don't exist, just as "information" doesn't exist. The "information" stored in the brain or on a floppy disk isn't information, it's just echos of experience. When one remembers, ostensibly it entails a convergence of many factors to contribute to the "memory"; given that precognition seems possible, even future events can contribute to "memories".

This doesn't answer your question; I suspect the question is unanswerable, just as "what causes gravity" is unanswerable. The universe isn't responsible for giving us answers to all our questions, but it does reveal the basic mechanics to us if we take the time to investigate.