Must the heirs pay the remaining amount of key money that their father had paid to the tenant, and how should it be distributed among them?

The old lease contract is invalid due to the unspecified term, and it must be فسخ (annulled) by enabling the owner to reclaim the property and the tenant to vacate without compensation, unless the tenant added something beneficial to the owner, in which case they should receive compensation for it, estimated by experts.

If the tenant agreed with your father on a "khalaw" (premium) in exchange for her additions to the shop, and for your father's benefit from these additions, then she is entitled to it. However, if the "khalaw" was merely for her departure to enable the father to sell the property, then it is usury (suht) that you are not obligated to pay.

If you strongly believe the woman is truthful and that she has a right to the "khalaw," then the remaining amount is a debt owed by your father and should be paid from the inheritance before its division. Similarly, if the woman insists on taking the remaining "khalaw" by resorting to legal means and you fear harm, then the remaining amount should be paid from the inheritance before its division. If the inheritance has already been divided, the money should be taken from the heirs, each according to their share.