I think the first thing you should do is get a copy of the accident report and see where they placed liability. If not stated, you need to get that changed. If he doesn’t have liability, you may be out of luck.
Need more detail of what happened but if they were directly behind you and you were moving forward even if you had to stop quick the person behind you needs to maintain a safe distance and have control of their car otherwise they are at fault. What does your insurance company say?
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