This is a common question, basically you splice them back to the wires on the harness but as you have lost quite a bit of insulation you are most likely looking at new wires.
First break into the harness and find the ends of the wire, cut them staggered, I don't like a splice next to a splice. I like to be able to tape the two wires together before the first splice, between the splices and after the second splice.
Get your new wires, Audi sell them ready terminated but only in yellow insulation. Or terminate some wires in the correct colours. Either way fit them to your connector.
Cut the wires to length and splice to the main harness.
Method 1, remove insulation from last 5mm of mating wires and tin the copper. Slip a heat shrink tube on, preferably the adhesive type. solder the two tinned ends together side by side. slide over the tube and shrink to insulate.
Method 2, Audi workshop method. get a couple of crimp with adhesive splices. Strip the insulation, crimp the splice, heat shrink to secure and seal the splice.
Tape before the first splice, between the two and after the second.
Tessa tape or tube main harness. If it is tube, splice and tube before fitting the terminals to the connector.
Will get pictures if that helps, if you need the car for Monday break into the main harness and see where you stand with wire lengths. Your local Audi dealer may have the wires in stock. They may even give you a couple of connectors, mine used to.