The good news is that the dimensions of the castings,(shell, inner cover, outer cover) stayed the same. Any plunger box will fit any plunger motor.
BSA were never radical when it came to change, they implemented relatively minor tweaks over time, fettling and improving the original basic design. The extravagant lifestyle antics of the top management had a lot to answer for.
The later plunger box cover, as yours appears to be, has the grease nipple and the kickstart spring will be the wire wound type, see the locking nut for the spring retaining bolt next to the kicker shaft, at the back.
The cover is certainly later than your Longstroke motor. But as the covers interchange, the rest of the box could be from the time of the motor.... or a complete later box entirely.
Swarfy.