From what used to be the FAA Inspector's Handbook and is now called F-SIMS (Flight Standards Information Management System) -
D. Night Restriction. Some foreign pilot licenses contain a restriction that prohibits the person from operating an aircraft at night. As an example, some foreign CAAs require their citizens to hold an instrument rating and/or a night flying privilege to operate an aircraft at night. That person must also comply with that night operating restriction of his/her foreign pilot license when exercising the privileges of the §
61.75 U.S. pilot certificate (see §
61.75(e)(3)). To clarify, while the FAA may not remove the night flying restriction, it is permissible for a foreign pilot who receives a U.S. pilot certificate on the basis of the person’s foreign pilot license to accomplish the required night flying training (for the appropriate grade level of U.S. pilot certificate held) from a holder of an FAA flight instructor certificate, and receive a solo endorsement to exercise night flying privileges on his/her U.S. pilot certificate.
As Silvaire said, your JAA license does not limit you to daylight hours. What you will have on your FAA cert is
“ISSUED ON THE BASIS OF AND VALID ONLY WHEN ACCOMPANIED BY [NAME OF COUNTRY] PILOT LICENSE NO. [NUMBER FROM FOREIGN PILOT LICENSE]. ALL LIMITATIONS AND RESTRICTIONS ON THE [NAME OF COUNTRY] PILOT LICENSE APPLY”
There's no night time limitation on your JAA license so I'd say there's no limit on your FAA cert even though the reason you don't have a night restriction is you have a JAA IR which you may not have the time to transfer to the FAA cert.
As I said in your other thread, you'll need a flight review before you fly under the FAA cert. The flight review must be a minimum of one hour ground review and one hour flight training. If I had a 61.75 pilot show up for a flight review I'd spend 2-3 hours reviewing stuff, airspace, how to get weather, ATC procedures, etc. Worse case, you do the flying part of the FR at night (I don't know if you need the whole 3 hours night training just for a solo signoff.) I used to do an hour of T&Goes and a short X-C to a controlled field about an hour away. Fill squares for the the student's X-C time, night time and controlled field operations all at once.