Is the lender entitled to demand the promised profit amount from the debtor's heirs, given that the debtor had fully repaid the principal before his death, and the third party did not deliver the profits to the debtor?

The question implies that the agreed-upon transaction, Mudarabah (profit-sharing), is impermissible due to the lack of capital guarantee and because the profit is a shared percentage, not a fixed amount. Additionally, in Mudarabah, the contracting parties are partners in both profit and loss.

As for the third person who joined you with your permission, there is no objection to that. However, your companion (the first party) is not entitled to any of the profits because he was acting as an agent at that point. There is no harm in agreeing to pay him a wage for his agency. But if he stipulated a share of the profit for himself, the contract becomes void, and the third person is then entitled to a fair wage (اجرة المثل), with all the profit belonging to you.

Regarding your claim against the heirs of your companion for the profits he agreed upon with the third person, of which he did not hand over anything, this is not permissible for you. This is because your companion was acting as your agent in the transaction, and the agency became void upon his death. However, you may claim the profits from the third person if you wish.