If a son sells gold ingots inherited from his father, and gives their value as zakat, would this absolve the father and the son from the zakat obligation due on them, knowing that the father had not paid zakat on them for 45 years, and they met the nisab then, as they do now?

The fundamental principle is that a Muslim pays zakat. If an heir doubts whether his father paid zakat on gold bars, the original presumption is that his father's financial obligation is absolved, and no zakat is due from the heir. It is permissible for the son to benefit from the inheritance, and he is not obliged to donate any part of it as charity. If he sells something and donates its value, he will be rewarded for it. However, if he is certain that his father did not pay zakat, then what was due from his father in zakat must be calculated.