Is a lapsed Advanced Ground Instructor certificate acceptable to use as proof of FOI when taking CFI initial?
That would be 61.183(e)(1):

To be eligible for a flight instructor certificate or rating a person
must:
(e) Pass a knowledge test on the areas listed in Sec. 61.185(a)(1) of
this part, unless the applicant:
(1) Holds a flight instructor certificate or ground instructor certificate issued under this part;