The subtle continuum is called the bhavanga or alaya vijnana and various schools have differing theories on it depending on their obsession with Emtpiness philosophy.

The Buddha did not know any of his past lives before the night of his awakening! It was all discovered with the super cognition of the samadhi states, just like many meditators after him. The Vishuddhimagga actually teaches people how to access subtle memory from past life imprints, and is taught in Sri Lanka to this day!