You don't have to take the FOI again. When you send in your test results for the AGI certificate the FAA will keep them on file in Oklahoma City. If you have your AGI it should be satisfactory evidence for the examiner, however if they want your FOI test results they can get them from Oklahoma City.

When I got my IGI certificate I took the FOI + IGI and then held on to the results until my CFI checkride. I filled out two 8710 forms, one for my Flight Instructor certificate and the other for the Instrument Ground Instructor certificate. Both certificates were then issued at the end of the checkride from the FAA examiner. I recommend doing it this way if you can wait for your AGI.