Fiqh-us-Sunnah Volume 2, Supererogatory Prayer, Fiqh 2.026A.
Section : Making qada’ for the missed tahajjud.
Muslim records that ‘Aishah said: “If the Prophet sallallahu alehi wasallam missed the late-night prayers due to pain or anything else, he would pray twelve rak’at during the day.”
‘Umar reports that the Prophet sallallahu alehi wasallam said: “Whoever sleeps past his full portion [of the late-night prayers] or part of them, he should pray between the dawn and noon prayers and it would be recorded for him as if he had prayed during the night.” This is related by the group except for al-Bukhari.