I wrote a review on the SHOM, which is here:
Please give us your movement number, it will be a more accurate way to date your watch.
The SHOM houses the Cal 478. And it seems it is the 479 ( also housed in the WWW JLC British military watch ) for the 2982B. According to the manufacture, the Cal 478 was in production from 1945 to 1965.
I tried to see if the case back could give us an information, but it seems they are similar. Not E for the 159, as it is not screwed in, but snap back case. Same for the 2982B, by the way.
Here the 159 SHOM ( not E, as it is not screwed in, but snap back case. Same for the 2982B, by the way ).
Now the Front: I wonder if the lugs are not slightly different, a side shot would help of the 2982B

SHOM:
So, the case similar or at least very close, but the movements are different.
Sorry to not be able to help you more nor better, here...
Best,
Nicolas
PS Credit picture of the 2982B: analog and Shift.