Yes it can be done but you end up with a wildcat cartridge, because the shoulder of the 375 Fl, is farther back toward the flange than the shoulder on the belted version.

This is done by boreing out the BELT area of the chambers, and installing a rings of steel, then cutting it flush with the end of the barrels, and running the fl reamer in to cut the ring to the Flanged base, cutting the recess for the flange, and the extractors. Then the 375 FL brass is fire formed to the resulting chamber. The rounds will have to be loaded with standard 375 H&H dies, or special cut wildcat dies. Since all double rifles need handloading to get the best they can offer, the use of a wildcat, this easy to make wildcat is a good choice. Because one can simply use the 375 H&H load data, starting with the low listed loads, and working up to get regulation, this one makes sense in a double rifle. However this work is not cheap, unless you can do the work yourself, and if not, it is easier, and cheaper to simply buy what you want from the maker, in the first place, but it can be done successfully,
if that is the route you want to go!