>>2978427See the two holes on the neck side of the shoulder? Thread gets in here, holds the big fat grey button you see at the top end of the shoulder board.
Now, see the small strip of fabric on the arm side of the shoulder? The shoulder board has another, longer and thinner, strip of fabric under it. You weave it in the jacket's smaller and thicker strip, fasten it to the button, and then fasten the main part of the shoulder board to the button. Voilà!