Depends
Again, assuming FAA...
If the person already holds a basic Ground Instructor certificate, the Advanced and Instrument ratings can be added without retaking the FOI.
If by saying that they have a newly issued AGI, you mean they've got recently-passed exams for Ground Instructor, Advanced Ground Instructor, and Instrument Ground Instructor, and no certificate, then the person will have to retake the FOI before presenting themself at the FSDO for the certificate.