What is the ruling on the money I receive in full from my employer, even though the system stipulates the disbursement of only half salary during my study leave, and what should I do about it for fear of them discovering the matter later?

If the regulations stipulate your entitlement to half salary during the scholarship period, then you are not permitted to take more than that. You must inform the authorities, regardless of whether the wrongdoer is punished. Sheikh Ibn Baz was asked about the disbursement of overtime pay without assignment or attendance, and he stated that this is a reprehensible act and a betrayal. He added that what was taken through this means must be returned to the state treasury. If you are unable to do so, then you must donate it to the poor and to charitable projects, accompanied by sincere repentance, because it is not permissible to take anything from the Muslim treasury except through the legitimate channels approved by the state.