ORG 8232 is a "register number". The Italians did not use troop designations on their rifles. The register number was a letter/4-figure number combination. For instance, my "Roma" 91/41 has Axxxx (a Terni batch). In your case, the OR stands for "Officina Costruzzione, Roma" - the manufacturer - and the G is a batch designation. The OR series dates from 1917-18. So you have a Moschetto 91/24 converted from a long "Novantuno" number 8232 from batch G, originally made in 1917-18 by Officina Costruzzione in Rome.
There could (should) be another stamp on the forward side of the butt, on the opposite side of the sling roll from the number. Look for signs of overstamping, as it was standard practice to stamp/restamp replacement/reworked stocks to match the (theoretically) unique and unrepeatable register number on the barrel.
Patrick