You get an estimate of the damage. You pay the insurers. You get a quote from an organisation with the authority to sign-off the repair. You get the work done, pay them, and send the documents to the CAA with authority to deduct their charges. You receive the documents.
Insurance companies write of aircraft which are readily repairable, because they don't want the responsibility for problems which arise. Often the owner will buy back the wreck and repair it. He usually is given first offer.