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):