You can try to solder the ribbon back together, but most likely it won't work. The more logical option would be to replace the ribbon with new wires. In the picture it looks like two leads on the main CB. If you use a light, flexible wire it is possible. If the ribbon is attached directly to the recording head and will be moving around then you will have to make sure you use some type of wire that wan't cause much resistence or the head will not move.
I have heard of using cheap headphone wire to do the trick on portable cd players. Otherwise the only way to fix it is to take it to a repair shop, usually costing more than is justifiable. Just don't use a singke core wire becouse it will wear and break. I have heard of the recording head ribbin breakng, especially when the record head is attached to the same carriage as the playback head. This causes the recording head ribbon stress while recording and during playback.
Hopefully you can bypass ribbon with a good, super light , and flexible wire.