How to capture additional information and have it linked to/accessible from, a Lead record and then the converted Potential record?

How to capture additional information and have it linked to/accessible from, a Lead record and then the converted Potential record?

We collect a good deal of information from each lead (via an online questionnaire, or during a phone conversation).  I've created custom fields within Leads to capture the info.
However, when the lead is converted to a Potential, there is no way to access that info.  I would like to know the best way to handle this data:
1.  Can I map the same custom fields into the Potential record for each converted Lead?
2.  Or should I create a Custom Module that stores this information for each Lead/Potential, and somehow link the record within my Custom Module to the Lead Record, and have that link automatically remain with the Potential record when the Lead is converted?