Fictional invoicingComprehensive damage after verification of professional repair in self-service

Hello to all I had a patrol damage with the guardrail. I am fully insured. An expert was also there for damage detection before the repair and has the damage to 610€ or roughly 5100€ without VAT, the replacement value to approx. 11200€ without VAT 9300€ and the residual value to 690€. I have repaired the car myself professionally, since I am from the specialist. After the successful repair came again an expert, which was sent by my insurance to the R eparatur to inspect. He confirmed,the absolutely perfect execution of the repair on the vehicle. My insurance nevertheless only wants to pay the replacement value minus the residual value, with the simple reason that I provide them with a repair invoice, otherwise there are no further payments.Whether the vehicle according to expert report and specifications has been professionally repaired. My question is, it is not enough, according to the law, that the car again more specialized has been repaired in order to have the sum less the VAT paid out according to the opinion ?