Kev, the 4 "pins" fit the rear cap of the case here
View attachment 111182
If you look carefully at the Bristol LMB reconstruction (made by Tony Boyle, a WW2 RNVR Render mines safe officer) it shows a central lug inside the case to which the parachute strings are attached - but no fins
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This is a similar system similar to what can be seen inside air-dropped flares. (British air dropped mines, when equipped with chutes, had a different system with attachment lugs around the end cap)
I am quiet suspicious about the Russian drawings (the English B&W drawing in the previous post is based upon the original Russian color drawing) showing a tail finned mine inside a bulky case.
Hope this helps.