When must the liability pay?

Hello together. At the beginning of the month someone damaged my parked car. The police took the accident. After consultation with the accident opponent I contacted the insurance and after consultation I ordered an expert report. Reports and police report are available to the insurance. A demand at the insurance showed that everything was available from my side. Only the damage report of the causer is missing. He has not yet reported the damage to the insurance. The clerk, however, very nice and understanding, said that without the damage report from the U-causer a regulation is not possible easily. When does the liability have to pay? I do not assume that it can take so long for the policyholder to report. That could then be xxx months, if any, until then. Thanks for information