can't be done in 90 mins if you haven't checked bags through.
I do FRA often and annoyingly BA often uses the northern runway (like yesterday) which means 15-20 mins taxi to T2 and often uses bus stands (yesterday was gate but that was first time for me in 20 odd flights). even ignoring those, you walk a mile or so from gate / bus drop via passport control and baggage and bags can be a bit of a wait (10 mins) yesterday. the transit to T1 is fine but again, takes 10 mins at least (getting there, wait, transit itself etc) so there's 0 chance of you making the check-in / bag drop cut off at T1.
if you can check bags through and have onward BPs, you can stay airside but I'd even then be nervous about 90 mins T2 - T1 (and probably even if it was a T2 - T2 connection on an unprotected ticket).