Your "Fritzbox 6660 Cable" is a COMBO modem and router.
"some kind of converter" is called a standalone cablemodem - something like this:
https://www.surfboard.com/products/cable-modems/sb8200/
Note that when you change the device connected to the cable (modem), you will have to contact your ISP and give them the MAC address of the new modem to register in their network so that it is allowed to connect. Some ISP's may have a website where you can log in and do this, others you may have to just call.