Without seeing the mod in its full glory, I cannot see how this can be soldered on! Can you take a photo of the cap at a 90 degree angle, so we can see it from the side. The reason why I say this, is the spring on the top of the LED board will press against the cap, and will put the solder joint under resistance. Also I am stabbing at stars here, but the wire looks like it is an earth wire, that just has to be connected/soldered to the cap.
The solution, dependant on the side of the cap, might be to drill 2 small holes and put 2 small grub/tapping screws through the body and cap.