What is the ruling concerning money that some people deny or claim not to possess enough of to pay, when my deceased father had a debt or an unrecorded partnership, so should it be forgiven with the intention of ongoing charity for the father, or is it accounted for by Allah as a right of the heirs?

As for debts and monies that are acknowledged, you have the right to claim them unless the debtor's destitution is proven, in which case he must be given respite, according to the Almighty's saying: "And if there is one in adversity, then [let there be] a delay until [a time of] ease. But if you remit [it] as charity, it is better for you, if you only knew."

However, for what is not acknowledged, it is considered a claim and must be brought before the judiciary to establish rights with evidence, as the Prophet (peace be upon him) said: "If people were given according to their claims, men would claim the blood and wealth of others, but the burden of proof is on the claimant and the oath is on the one who denies."

If the judiciary rules in your favor, then forgiving the debtor is a good deed for which you will be rewarded.

As for making those funds a perpetual charity before collecting them, it is not permissible, because what is in someone's liability cannot be endowed.