Although it was really a parallel development to our own M14. Uncle Sam gave Italy the Winchester M1 Garand tooling line, and Beretta (among others) began producing their own M1 Garand - which in some respects was an even nicer gun than our own domestic manufactured rifles.
When the 7.62x51mm NATO round became the de-facto standard for NATO members, the resourceful folks at Beretta decided to use as much of the M1 Garand tooling as they could while making a detachable, box-fed magazine rifle in the new 7.62mm NATO round. The result was the BM-59, a rifle that used the M1 Garand's receiver, with a special magazine for the 7.62mm NATO round (Not BAR, Not M14, but a unique BM-59 mag) that fit nicely in the space normally reserved for the M1 Garand's magazine well for the 8-round en-bloc clip of .30-06 rounds.
I own a BM-59 and several of those mags. They aren't cheap, and they're nothing like either the BAR or M14 mags. The BM-59 mags fit rather nicely in the M1 Garand's receiver space, and one can tell it took only a minimum of receiver modification to accomodate the 7.62x51 length magazine, a couple of tack welds or shelves/ledges in the forging, and voila'!
A conversion of an M1 Garand to use M14 magazines would probably go the same route, because, again, the M14 is chambered for the 7.62mm NATO round - considerably shorter than the .30-06 round the M1 Garand was originally chambered in. The magazine is short enough to fit in the M1 Garand receiver without removing critical metal.
An M1 Garand modified to take Browning M1918 BAR magazines, however, is an accident waiting to happen. BAR magazines are .30-06 length. Add the BAR .30-06 magazine's external dimensions to the equation, and stuffing it into an M1 Garand's receiver area requires grinding away a goodly amount of metal for magazine clearance. That's metal intended by John C. Garand to keeps the gun in one piece and the shooter safe.
I've seen M1 Garands hacked to accept BAR mags. Not pretty, and I sure as heck wouldn't shoot them with that much steel removed in the receiver.
