Musannaf Ibn Abi Shaybah 6513 — A man who begins praying at night

Ja'far bin Burqan said: I said to Maymun: I recite a long surah in the night prayer and the morning comes upon me during it, until it becomes light; may I then join another rak'ah to it and make this prayer the sunnah of Fajr? He said: Yes, you may.