What is the recommended time for making up missed night prayers (Tahajjud)?

Primary text

It is recommended to make up any missed portion of the night prayer (Tahajjud) between the Fajr prayer and the Dhuhr prayer. This is established by the saying of the Messenger of Allah (peace be upon him): Whoever sleeps through his portion or some of it, and reads it between the Fajr prayer and the Dhuhr prayer, it is written for him as if he read it during the night. The practice of the Prophet (peace be upon him) when he missed his vigil during the night or was sick was to pray twelve rak'ahs during the daytime. This practice is supported by the actions of the Prophet (peace be upon him) as reported by Aisha.