Yup, fits (at least without a J-type OD, not sure about with a J-type).
You might need to replace the 3 studs along the top with longer ones.
If you still have the stock TR4 clutch, you might want to swap over the front cover (which is slightly longer on a TR4). However, the factory apparently said the shorter covers could be used with the earlier clutch, so perhaps it's not necessary (but I did).
IIRC, the TR6 box used narrow bushings for the clutch shaft to ride in, with no provision for lubrication. I chose to install two of the wide unslotted bushings from a TR3, plus drilled and tapped for grease zerks. You can drill & tap the shaft ala TR3/4, but I found it easier to do the case instead (plus the Stags have no clearance for zerks on the shaft).
If it's a late TR6 box, the speedo drive gears will be wrong. For non-OD, I believe you can just change the driven gear in the side to get the TR4 ratio.
Can't think of anything else offhand ...