New question on SFR adoption

Hello, my father passed away the year before last, at that time we did not take care of the car re-registration and insurance re-registration. The damage-free discounts are to be preserved. The insurance broker proposes to keep running car/insurance on my father’s name, because if we now re-write car and insurance on my mother, then perhaps the car insurance of the SFR transfer with reference to the expired deadline would not agree. The broker also said that the transfer of the SFR would work on a car re-registration. I think this is risky, because the insurance could refuse post-payment or performance. What would you do now? Thank you in advance.