The filter ring on the J-3 is not removable. On some lenses- such as the Nikkor 5cm F2, it can be unscrewed and replaced.
You are left with a choice of "hacking" a step-up ring into the lens, which I've done on some lenses. OR- with as many bad-glass Jupiter-3's out there, get a fixture and transplant the glass into it. That's my preferred solution, I've done it on a number of them.
You need to get the correct fixture. KMZ glass can only go into KMZ fixtures, and they are all the same. Early ZOMZ lenses, 1956~(ABOUT) 1963 have a rear fixture to hold the triplet in place, it screws into the main barrel. Lens on the left is complete, one in the middle shows the triplet removed. Later lenses have a one piece fixture, on the right. I've interchanged glass between Valdai and ZOMZ "onesies" before.
You will need a spanner to remove the retaining rings, and possible a suction cup to pull the middle triplet out. If you get a complete lens with just a bad front element, you can usually just replace that. Makes it easier. After transplanting glass, a fine-tune to the shim is usually required.
It is best to unscrew the barrel from the focus mount and verify the type, whether or not the rear triplet is in the separate fixture. After 50+ years, someone might have been doing some swapping around. Kind of like I do.
Focusing on the pin in the middle orange you can see the focus is somewhere behind that in both the Jupiter and the Sonnar. The Leica lens was just to check the camera rangefinder is properly calibrated.
M9 and Kipon adapter.
That gives a good idea of how far off the focus is.
As you have the full-res images, how many centimeters do you judge the back-focus to be?
I have a formula for converting back-focus to increase the thickness of the shim. Getting the value for your camera is critical.
We'll call this the incredible Jupiter-3 Glass Transplant... The 1962 and 1961 J-3 were quite close, some slight differences. But close enough to transplant the front element, rear triplet, aperture ring, stand-off ring into the good barrel. Used a fairly thick 1.6mm shim, and re-indexed the aperture ring. The helical was loose in the mount on this lens- it was recently lubed. The three set screws visible once the focus ring is off required tightening. This fixed the slop in the focus, is quite nice now.
All shots wide-open, with the RF of the M9. This lens can be used from close-up to infinity, wide-open.