Is it permissible to perform the night vigil (qiyam al-layl) and recite the Qur’an during working hours, and is the one who does so rewarded, even though he does not wake up from his sleep to perform these acts of worship?

The employee whose benefit is measured by time is a special employee, and all his benefits during the work period belong to the employer. He is not permitted to use this time except for work-related matters. However, if your employer grants you permission to utilize a part of your working hours for whatever you desire, then there is no harm in you performing night prayers, reciting the Quran, reading a book, and so on. As for the reward for night prayers in this situation, you will be rewarded for your prayer because you pray with the intention of praying, not with the intention of staying awake, as you could stay awake without praying. It has been reported in the Hadith that whoever wakes up at night and prays, his prayer is accepted, and this includes anyone who takes advantage of their wakefulness for prayer or remembrance.