This question pops up frequlently,I think the problem dates back to 1934 and the Fed 1,which was a remake of a 111B. I have three J lenses none of them will focus correctly on my III G, however on my III C , everything works just fine. The reason for this is that the III C has thicker wheel on the rangefinder arm. I recomend two simple tests: First, scale focus at at a test target from wide open and down, and then rangefinder focus at then rangefinder focus at the same target. If scale focus is sharp, your back focus and lens elements are placed correctly in the barrel. To check if the focusing ring or peg mates with the wheel on the focusing arm,use an old mechanics trick. Put a thin layer of Prussian blue ( or even lipstick) on the wheel and mount the lens. The peg should leave a marking on the wheels OD.
Best regards,and wish you luck. Henry.