Does what the eldest brother did – taking half of the rent from the shop and the house after the father's death, claiming partnership without proof – conform to Islamic law? What is the ruling on selling the property and distributing the inheritance of the eldest brother?

The default rule is that the father's estate is divided among the heirs according to their legally prescribed shares. The brother's claim of partnership with the father requires evidence or an acknowledgment from the heirs; otherwise, it holds no weight. The heirs' silence out of shyness is not considered consent. Therefore, the estate should be divided among the father's heirs according to their legal shares, and the share of the deceased brother should be divided among his heirs. If there is a dispute, it must be referred to a Sharia court or to scholars for their guidance.