Is it permissible to benefit from money earned from the father's work in a commercial shop rented under the old lease system, with a portion of the money being paid to the heirs of the first tenant, and what is the ruling on this money?

The basic principle regarding a Muslim's wealth is that it is pure and earned through lawful means. One should not deviate from this principle except with certain proof or a strong presumption. Mere doubt does not prohibit interaction. Ibn Taymiyyah stated that if a Muslim knows the condition of usurped or unlawfully acquired property, they should avoid it, and it is not permissible to take it from someone who seized it unjustly, because it is precisely the property of the wronged person. However, if a Muslim does not know the condition of the wealth in another Muslim's possession, the matter is based on the original principle. If a man is known to have unlawful elements in his wealth, one should refrain from dealing with him out of piety. There is no doubt in dealing with a righteous Muslim at all. The mentioned possibilities are mere conjectures that do not rule the father's wealth to be unlawful.