Thanks for you help; it worked perfectly fine!
If anyone wants CyanogenMod File Manager backport with root access on the Fairphone—First, download the BusyBox Installer through APK Downloader, as described above, and install it on your phone. Next, install the app “/system/app mover” as well as the CyanogenMod File Manager backport, using F-Droid (https://f-droid.org/). Use the system app mover to move FM to the system app folder (not sure if this step is necessary) and then, in the FM settings, switch to its root access mode. Now you should have full access to and options/rights to all system folders. Great!