Is it permissible to consider the money spent on the family from the scholarship allocated in the wife's name as Zakat al-Mal, and what should be the intention for Zakat in this case for the future?

The salary granted by the state is not subject to zakat unless a full year has passed on it, and it reaches the nisab on its own or by combining it with other money. If you wish to pay zakat from other money you own to your husband, it is conditional that you first take possession of your share of the salary. Then, you may give it to your husband with the intention of zakat if he is eligible, such as being poor or needy and unable to provide for his basic needs and the needs of his dependents. However, if your husband accompanies you for your benefit, it is not permissible to pay zakat to him because his expenses would be your responsibility, as he is prevented from working for your sake.