[fredjacksonsan]

I don't know about the price for the backup sensor, but:

There's no way they can prove that the damage that has been done resulted from your collision, since they could have backed into something or been hit again since the October incident. It's too late to report to insurance companies, since most require a report within 30 days.

As I see it, there are a couple options:

1) Tell them it's too long after the accident, and anything could have happened in between.

2) Suggest they report it to their insurance company.

At this point, since neither company will pay on the claim (probably) they will have to sue you in court to recover the cost, IF, that is, they can prove that you hit them. Did they take any pictures? Is there a police report? Has the damage to your vehicle been repaired?