Is it permissible to give zakat on money to a relative who is unemployed in Syria and has a wife and children, knowing that his wife works but her salary is not enough for their needs, and should the amount paid be for a year or not?

The basic principle is that it is not permissible to give zakat to a strong person who is able to earn a living. However, if they cannot find work, it is permissible to give them zakat, as they are then in the position of someone unable to earn. If their income is not sufficient for their basic needs, it is permissible to give them zakat; moreover, it is more deserving due to kinship, and it becomes an act of charity and maintaining family ties. There is no harm in transferring zakat to them for an overriding benefit, and they should be given from it what suffices them for one year.