It would be no different than a 9mm conversion. I did this with my Uzi.
The only thing you would need in addition to a 9mm conversion would be to open up the bolt face ever so slightly. You can probably get away with it as-is. Depends on the condition of the bolt. The rim on the .40 is so close to 9mm that a used bolt may require nothing at all. My Uzi "opened up" after about 200 rounds, and it "just worked" with .40 after that.
You can also use the same magazines as with a 9mm, albeit with a slightly lower capacity.
It would work!