If such a condition is specified in the contract (or in the company's internal documents) that payments are not made without submitting a medical report on death, then the actions of the insurance company are legitimate. You can provide them with a medical certificate of death - this will be the confirmation.
Also, the insurance company can independently submit a request to the medical institution regarding the occurrence of an insured event regarding the insured person, that is, your father.
On 04/04/2023, the Verkhovna Rada Committee on National Security, Defense and Intelligence issued a decision to recommend that the Verkhovna Rada adopt the Draft Law on Amendments to Article 26 of the Law of Ukraine "On Military Duty and Military Service" on expanding the grounds for dismissal from military service of some categories of citizens during the period of martial law". The project provides for the introduction of grounds for dismissal from military service of military personnel whose close relatives died in the war or went missing. Therefore, there are chances that these changes will be made to Article 26 of the Law of Ukraine and approved.
In accordance with the Law of Ukraine "On Court Fees" dated 07/08/2011, as amended on 03/31/2023, a court fee of 150 percent of the rate that was payable upon filing a claim must also be paid for filing an appeal against a court decision. , other statements and complaints. For filing an appeal against a court decision, the court fee for individuals is 0.2 of the subsistence minimum for able-bodied persons.