How to change the relationship of a record from one module to another

Sugar On Demand | 9.1 | Professional

Our Flow & Some Background Info:

Unclaimed Lead(Leads Module) -> Prospect(Opportunities Module) -> Current Account(Accounts Module)

Our marketing department uploads pre-qualified leads to our 'Unclaimed Leads' module. Our sales team(users) then  pick and choose leads and convert them to a Prospect to begin the sales cycle. When the lead is converted, the user creates a contact record and a prospect record that are related. Once the sales stage is Closed Won, the prospect then converts to a current account via a logic hook.

My Question:

Everything is currently working as it should, however the issue I am running into is once a Prospect converts to a Current Account, how do I take the contact that was linked to the Prospect record and link it to the new Current Account record?

Thanks in advance for pointing me in the right direction.