The Italian prop may be bigger in diameter. Propellers have to be not only matched to the engine but to the speed range and operating altitude of the aircraft.
High speed aircraft can use smaller diameter propellers than larger, slower moving aircraft. Large, heavy aircraft need their propellers to move a large quantity of air, but they need the propeller stream to be matched in velocity to the speed of the aircraft.
While US fighters with 2000-2300hp P&W engines used propellers of around 13 feet in diameter, the Lockheed Constellation used 3 bladed propellers of over 16ft for it's 2000hp R-3350s and the B-29 used 16'7" 4 bladed props for it's 2200hp R-3350 engines.
The larger, heavier airplanes may need bigger propellers for better take-off and climb performance even if they hurt top speed by a percentage point or two.
While the Germans could certainly have built a propeller of their own and not used an Italian manufactured propeller the propeller would have to be a close match in performance to the original. as I said before, this might require using a different gear ratio on the Jumo engine.