International MMSI numbers belong to the boat, not the owner. You cannot transfer them to another boat. So, you need to get a new MMSI number for the new boat, and you need to cancel the old one or have the new owner use it to update the records.
Same thing for the FCC ship's station licence, if you have one. The radiotelephone operators permit
, however, belongs to you and is valid for life.
None of this has anything to do with EPIRBs. EPIRBs have their own unique identifying number, registered with NOAA. You need to update the EPIRB registration with NOAA so it shows the new boat. Here's the website: