Sorry, this probably isn't what you want to hear, but I've seen this situation a few times before. Personally, I would ask them if you can replace the fence.
It's also worth bearing in mind that composite fencing isn't always the ideal long term solution. Even products sold with long guarantees can start to look tired, weathered and quite industrial after a few years.
I would also avoid leaving a gap between the two fences. In my experience, it quickly becomes a maintenance headache. The space tends to fill with weeds, bindweed and ivy, which grow through, under and over both fences. Unless you leave a significant gap, it's almost impossible to access the area properly for maintenance.
Having dealt with this myself, the only practical way to keep the area clear was to lift the fence panels, prop them up and then weed between the fences. It's time consuming and awkward. The gap can also provide an attractive shelter for rodents. If you are going to do this, concrete the ground between their fence and yours.
From experience, replacing the damaged fence is usually the cleanest and most practical solution in the long run. In addition, you don't have the headache of boundary arguments in the future.