Hi Jamie,
First of all, this adaptation has been doing by many, both factories and gunsmiths. Like the most famous of all because the cartridge, Holland & Holland.
If that action is set up for a short, or standard, magnum cartridge, like the 7mm Rem Mag or 300 Win Mag the only, but critical thing to do is to lengthen the action and magazine for the longer cartridge, the 375 H&H. I said critical because this machining MUST be do without weakening the action in the low stop for the right bolt lug. So, this MUST be do by a GUNSMITH who knows what he is doing.
Looking at an authentic Holland & Holland 375 H&H made on a Standard M98 Mauser Action is an entire education on this. Period.
Good Luck!
CF