It is possible to use internal SIP accounts of Fritzbox as "line" for Gigaset T300/500 PBX.
For the provider settings have a look here:
Have attention to the following remarks too, please…
1. For each Fritzbox telephone a separate Provider has been to setup in the Gigaset T300/500 PBX:
2. For the number use the Fritzbox number (=Username):