Is it permissible for a husband to slaughter an animal for the sake of Allah Almighty with the intention that his wife, whom he divorced under duress, returns to him, and if that is not permissible, then what is the solution to what has befallen him?

It is permissible to slaughter an animal as an offering to Allah Almighty with the intention of your wife's return, for interceding through righteous deeds is legislated, and slaughtering for Allah is one of them. However, giving the price of the slaughtered animal in charity, or other forms of charity, might be more beneficial and greater in reward. Supplication is beneficial and a great act of worship, and the Prophet, peace and blessings be upon him, said: "There is no Muslim who supplicates with a supplication in which there is no sin or cutting off of kinship ties, but Allah will grant him one of three things: either He will hasten his supplication for him, or He will store it for him in the Hereafter, or He will avert from him an evil equivalent to it." Entrust the matter to Allah, for what befell you was not meant to miss you, and Allah knows what is best for you.