For this mod, I used the Joye510 atomizer (aka Janty Dura, Yeti, Titan, etc.). So far, we have not found anything to match the size and thread pattern of this atomizer, so I "liberated" my connector from a factory 510 battery. This can be done with any model except the cigar and the pipe so far. The center is always positive and the outside is always negative.
I took the connector apart to do my soldering because that is easier for me, others solder it with the two parts still connected. I also wanted to show the two parts separated so that others can see the two distinct parts and where the connections really are. Here are pics of this process.
It isn't visible in the pics, but there is a hole through the center of the center, positive part. I inserted the wire into the hole and soldered it there, making sure to completely fill the hole so I could drip to my heart's content without dripping into the box (just a personal preference, others might not approve of my overuse of solder - you can use caulk or epoxy if you prefer).
I soldered the negative wire to the outside of my connector. The factory solders it on the inside edge, but I don't have that precision in soldering. I apologize in advance for the sloppy soldering job as this is the second mod with this connector and I did not remove the previous solder prior to doing this one (lazy and hurrying and not really skilled at soldering yet).