This appears to be a simple 2 conductor adaptor. Assuming that this is correct it should be VERY easy to fix.
Strip the wires back a few inches and slip on 2 pieces of heat shrink tubing (one for the center splice and a larger one for the outer shielding (negative or ground side))a bit bigger than your splice will be and splice the center back together using solder to make a secure connection, then use the heat shrink tubing (only on the center wire) to seal the center off from the outer layer. Then repeat for the outer shelding. Because the outer part will be difficult to solder I would advise using aluminum foil with the conductive side out (you can test for this side using a volt meter that tests for resistance and look for 0 ohms) wrapped on the outside of the center (now sealed) wire then lay the outer strands over the foil - the point bieng that a good connection is made between the 2 sides of the shield (strands) while using the foil as insurance.) Then use the heat shrink tubing to complete the clean-up.
Use a meter to test as much as you can (understanding that it will not be easy with the adaptor in the way) will help from having to do it all over.
Sorry if this is confusing, I hope it helps. This is actually really simple to do, but done correctly will still look very good and professional. All the parts are about $2 for the solder and heat shrink tubing. A soldering iron is $10, the heat shrink tubing can be activated (shrunk) with a good hair dryer or a lighter (be careful with the lighter).
Good luck.
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