UPS indeed only goes internationally as far as I know and otherwise takes StarAir. But FEDEX already flies within Germany, they have a trip CGN-ATH-TLV-MUC-CGN. This route is operated by B757 since they´ve taken it over from the Airbus. I believe they also operate a CDG-CGN-MUC trip by B757.
This is similar to non-United States airlines operating routes such as [non-US]-JFK-ORD-[non-US].
In your example no freight can be loaded in MUC for CGN. Freight can be off loaded in MUC, and freight with a destination outside of Germany can be loaded in MUC and carried through CGN. But if FEDEX wants to move freight between MUC and CGN they will have to find another way.