Is it true that Abu Hurayrah, his wife, and his servant divided the night vigil (qiyam al-layl) into three parts among themselves, and is it better for all of them to pray during the time of Allah’s descent?

Performing [optional night prayers] in the last third of the night is superior, but for one who fears missing it, it is better to perform it earlier. This is indicated by the Prophet's (peace be upon him) recommendation to Abu Hurairah to pray Witr before sleeping.

Abu Hurairah, his wife, and his servant used to divide the night into three parts: one of them would pray, then wake the other. A group of the Salaf (early Muslims) also did likewise.

As for one who is confident in waking up, it is better for him to perform the prayers in the last third of the night when the Lord, blessed and exalted be He, descends. The best form of night prayer is the prayer of David (peace be upon him): he would sleep for half the night, pray for a third of it, and sleep for a sixth of it. Allah has described His believing servants as those who "used to sleep but little of the night [during times of worship] and in the hours before dawn they would ask forgiveness."