Sil is probably correct that you have a D-type. The J type's solenoid is found on the driver's side of the OD and has two spade connectors.

In my experience, the J-type has a large stock output flange that requires a special part to mate up to a standard 1.75" driveshaft. I had to order a special flange from Don Thibault and I had to modify a differential flange to fit the replacement rear when I put a J-type OD and an 1800E rear in my 67 wagon.

I'd look at it like this. The solenoid is wasted anyway and if you can fix it, you've saved yourself some cash and picked up a good skill. If you can't repair it, you are not out anything more except some time and effort.

If the wires from that solenoid exit through some sort of potting material, try removing that stuff (knife or dremel tool) and find the wires. Look for some bent housing bits that you can release to open up the casing. Once you are inside, hopefully you can find the broken wire and re-attach it.

If you succeed, I'd strongly suggest adding some sort of break-away connector on the wire to avoid this happening again.

If you have no luck or can't see how to fix it, contact BB member ODGuru. He's well-respected for his knowledge of the M41. Actually it would not hurt to contact him anyway.

If you try for a repair, take some photos for us.