Convert Lead to Contacts, what about the linked custom module data from the lead?

I have the following problem.

I have a custom module( e.g. samples module ), which is connected to the leads module. In the backend I am able to create 'sample' records, no problem here, but

When I convert the lead into a Contact I want to take the 'sample' records with me and store them at the contact level.

I do not see an option in the mapping ( Lead -> Contact )

So here is my question, how to link the custom module to both Leads and Contacts, so that
- I can create 'sample' records in both the leads and Contacts module
- Be able to take the 'sample' records attached to the Lead with me in the conversion to a Contact