Hi,
If there is a center hole from the back side then a piece of solid copper wire like a short piece from the stuff used for house wiring) can be sanded/filed to a point, tinned with solder and pushed into the center hole. Proper tapering and shaping of the wire would allow if to be pushed into the hole.
If you are "good" at soldering, then put an atty on the connector and solder the little piece of wire to the center conductor. The atty will absorb some of the heat and protect the insulator some.
I did one once with the copper wire and filed it down so it went all the way through the center pin and I could pull on it a little with needle nose pliers to get it in tight.
Then cut it off flush.
let me know if this makes
sense and if we need to analyze it more.
Rocket