Some say it doesn't work because the 44-40 case mouth is smaller in diameter. However I rechambered a 44 Mag cyl to 44-40 because it was so easy, I did it myself. Barely any metal is removed and the throats are already the correct size. And as Hashknife pointed out above, you'll need to use .429" or .430" (I like .430") bullets anyway if you want decent accuracy with the .429" bore. So the difference in case mouth diameter is diminished and the thinner walled, bottle neck shaped 44-40 cartridge seals well in the chamber.
Works perfectly in my gun with accuracy as good as the 44 Mags.