From the pictures it looks like just a spot is burnt and the wire is good on both sides of the burnt spot..
It"s possible that the wire was grounding out and that's all. I would first try, solder splice same gauge wire back in with weather proof heat shrink (the heat shrink with glue inside) to seal it. Cheap fix if it works and defiantly worth a try because you can't hurt it anymore than it already was.