Is it permissible to offer expiation for fasting on behalf of a deceased parent who missed two Ramadans due to illness and old age, and would that suffice for him?

We ask Allah for mercy and forgiveness for your father. If your father did not fast for two months of Ramadan due to his old age, and his inability to fast is continuous and there is no hope of his recovery, then he was obligated to pay a fidyah (expiatory feeding) of one poor person's meal for each day he missed (750 grams of the staple food of the people of the country). Since he passed away before paying it, it should be disbursed from his estate before its division. If you voluntarily pay it on his behalf, this is sufficient for him, and you will be rewarded for it.