Then have your daughter accept the car, say “thank you” and you can then take it to a mechanic yourself for an inspection. There is no reason to do that before he gifts it to your daughter so there is no opportunity to offend him.
Assume some money may need to be spent - a new set of tires since they are likely 10 plus years old and are no longer safe even IF the tread looks OK. I’d also flush the brake fluid, change the oil, change the transmission fluid and the coolant since ALL degrade with TIME as well as mileage. You can offer to pay for this or she can do it but it should be done.