The best time of the night to offer

Q 4: If a Muslim wakes up before dawn to offer Salah (Prayer), and then the Adhan (call to Prayer) for Fajr (Dawn) is announced while offering Salah; given that the Fajr Prayer does not begin except after twenty minutes, should one continue Salah or perform Witr (Prayer with an odd number of units) and then offer the Sunnah of the Fajr?

(Part No. 7; Page No. 223)  A: The time of Qiyam-ul-Layl (optional Prayer at night) and Witr starts from the `Isha' (Night) Prayer until the rise of dawn. If the dawn appears while a person still has some Rak`ahs (units of Prayer) to offer, or there is still the Witr to offer, they should offer the missing Rak`ahs in the morning before noon. This is based on what was narrated by `Aishah (may Allah be pleased with her), that the Messenger of Allah (peace be upon him) used to offer the Witr every night, sometimes in the early part of night, at midnight and in the late part, finishing his Witr at dawn. Agreed upon by Al-Bukhari and Muslim. Abu Sa`id Al-Khudry (may Allah be pleased with him) narrated that the Prophet (peace be upon him) stated: Offer Witr before the morning. Narrated by Muslim. Ibn `Umar (may Allah be pleased with him) narrated that the Prophet (peace be upon him) said: When dawn appears, all night and Witr Salah become invalid. Therefore, be keen on offering Witr before the rise of dawn. Narrated by Al-Tirmidhy. `Aishah (may Allah be pleased with him) said: When sleep or pain overpowered the Messenger of Allah (peace be upon him) and made it impossible (for him) to offer Qiyam-ul-Layl, he used to offer twelve Rak`ahs during the day. Narrated by Muslim. (Part No. 7; Page No. 224) May Allah grant us success. May peace and blessings be upon our Prophet Muhammad, his family, and Companions.