People have been saying/talking about the need to redo the verification and have the piggyback one re-issued again due to address change. Maybe just ONE voice on pprune quoting asking FAA and that certain fisdo guy/s said 'no biggie' in other words. Also, bear in mind, that if you have good redirection/forwarding of post from your old address, you can argue that the notifying FAA within month of address change, does not apply.
It's ridiculous, having to pay UK CAA for same thing that's been done before, but they follow the laws and keep charging for it too much. I, for example, had to redo the ICAO PPL verification for adding IR US test passed on validation PPL as I 'ran out of time/cash' last time and didn't do full FAA CPL(A). Something that's meant as 'temporary validation' isn't good long term and I know it.
If you change stuff within 6 months of the verification letter date, FAA still consider the letter 'current', so no need to get it again in short time.
In short as said above, different licence number, different 61.75 needed - new one.
bose-x saying 'different licence'. Well, for 61.75 purposes, it doesn't matter if you have CPL or PPL privileges on ICAO licence. What's important, is the class/category and less directly, night or instrument privileges. You can't exercise CPL privileges on FAA PPL ONLY validation anyway. So the 'all limitations and restrictions apply' is about the aircraft and conditions of flight, not PPL vs CPL.
Obviously, issued by same authority. If they moved your licence across states with same number, then the 61.75 wording would be 'off' by a country..