What is the ruling on the salary I will receive during my absence from work for study, knowing that I previously worked for five months without pay, and is it permissible to give it to my needy brother if it is not rightfully mine?

There is no objection to benefiting from the salary granted during the leave period, as long as the head of the department is authorized to do so, and provided that there is no strong suspicion of collusion with you or that he acted beyond his authority. In such a case, it is not permissible to take the salary except with the permission of the authorized person; otherwise, it must be returned to the employer. As for working five months without salary, if it was by agreement, then it is a voluntary act, but the head of the department might grant a bonus for that period.