In FAA Land every certificate includes the privileges of lower certificates: light sport < private < commercial < ATP. You may only exercise the privileges of any level with the appropriate medical.
One of the requirements to get a commercial certificate is to already have a private certificate. The 61.75 private ticket fulfilled that requirement.
In the OP's case, since the underlying license has changed and is no longer the same number referenced on the 61.75 private certificate, the private is no longer valid. However, since the commercial certificate is completely independent of anything else, it will function just fine indefinitely provided the holder does a current 61.56 flight review and has a valid medical. In FAA Land, EASA Land, or the rest of ICAO Land.
(The above would make him FAA-legal to fly an N-registered airplane. Local rules about keeping, owning, or basing N-reg in EASA Land will also apply.)
Enjoy flying!