Unlikely. But if you have access to your friend's insurance policy, read the exclusions.
There probably is an exclusion for damage to property used by the insured (your friend in this instance). If that is the case, the exclusion applies because the damage to your car occurred when your friend (the insured) was using it.
If he had property damage coverage for his own vehicle, it likely would cover your vehicle. Your question, however, states that he only had liability coverage.
Usually, but it will depend on the language of the coverage. I would file a claim and possibly consult with an attorney to evaluate the facts of the case. Best of luck.
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Generally the insurance policy covering a vehicle involved in an accident is "primary", meaning it covers the loss first, and a policy covering the driver is "secondary", meaning it only kicks in if the first policy doesn't cover the entire loss. This is true even though the accident was the driver's fault.