The timings of the phone's rotaty dial might be off. Allegedly FritzBoxes are rather conservative when it comes to these timings.
I just had the same problem with an old Tischfernsprecher W 48 which neither worked on a FritzBox 7560 nor a 7590. Adding a pulse to tone converter solved the problem.
Btw, in case pulse dialing works with a FritzBox one can dial # via hook flash. This allows to dial the internal numbers [0].
[0] (in German) https://www.wasser.de/telefon-alt/forum/index.pl?job=thema&t...