Assuming one wire from one coil is still connected to one wire from the other, the wire that isn't connected to the center conductor of the braided cable gets soldered to the braid or backplate.
Assuming one wire from one coil is still connected to one wire from the other, the wire that isn't connected to the center conductor of the braided cable gets soldered to the braid or backplate.
Your picture shows it being soldered to a wire running toward the white bobbin. Leave that connection as is and isolate it with tape or shrink tubing, etc.