Peel the coax cable. Leave original shield as shown, the longer the better.

      Insert a bigger clue heatshrink 1. Then insert a smaller heatshrink 2 and heat it until you can see the glue coming in sight.

Slide the bigger heatshrink and heat it until you can see the glue.

     Wind a choke balun (in this example 4 turns on Fair-Rite 2631103002)
and add scrimp lugs for antenna connection.