AFAIK, the process of memory belongs to the Sanna aggregate. Refer Ven Pannavaddho’s explanation.
How exactly Sanna (or for that matter, Vinnana) arise due to contact is not explained anywhere in the EBT. The nearest possible explanation is that these arise as part of the Namma- Rupa - Vinnana trifecta (SN12.65).
PS: Here is a modern day speculation ( Quantum/ non local! ) about where memory is stored!