I think all of these use SAE 80W90 gear oil. This mower is actually made by Sicma of Italy. Sicma makes a good quality mower that is sold under many brands: First Choice, Kleen Kut, Kioti, Phoeniz, Farmmax, Deere, and probably others.
I have a KK finish mower and it takes SAE 80-90 gear oil. thats a safe oil to put in. Its got about 4000 acres on it now with no gearbox troubles .. . John
Also, if you store your machine in the weather, cover the gear case vent to keep rain out.
I noticed the characteristic "white" (water in oil) in my rotary cutter grease when I changed it last fall because my cutter sat out in the weather. I'm sure a little water would eventually cook off with use but maybe not before starting corrosion.