How can I fix these broken wires?
Match and mark Wire positions ,
clean old solder joints with vacuum solder sucker tool or gauze wire to absorb solder and
clean out plated thru  hole.

Mark wire with ink for pin 1 so ensure same as original connections.
Separate and cut wire to staggered length with 2cm incrments.
Strip insulation to 1 cm so exposed wires do not touch adjacent joints.
Twist single pairs tight with fingers and some dexterity then solder and repeat for next.   

Solder as in https://www.youtube.com/watch?v=aoD2aUvnQXg after 13:40.    

Then insulate with Kapton tape or clear packing tape or similar    

For brittle solder wire on PCB , I use polyurethane subfloor adhesive from a caulking gun to make a plastic strain relief and mold some gunk around solder joint on board to prevent future failures after testing. 24 h cure.