Are the children of the deceased entitled to claim a share of the money their uncle will receive for waiving his right to the shop he was managing, given that their father had paid the advance rent, then their grandfather took over providing the goods, and subsequently the management of the shop transferred to their uncle after the death of both the grandfather and the father?

The summary of the answer: The father acquired the usufruct of the shop by renting it. An agreement should have been made with the grandfather that the father would be entitled to the market rent for the shop during the period the grandfather managed it. As for the monthly agreement between the father and the uncle, it is a binding lease for the shop, and the questioner has the right to demand this rent. It is permissible for the tenant (the father) to sublet the shop.

If the owner of the shop requests its return before the end of the lease term, there is no obligation to surrender it. You have the right to reconcile on a financial consideration for waiving the right of lease, and the money due as a result is your right, not the uncle's, and it can be demanded. However, if the contract term has expired, you have no right to the shop. If the contract was perpetual, it is void, and you are not entitled to anything upon vacating the shop. Such issues should be resolved in court.