The Messenger of Allah (peace and blessings of Allah be upon him) said: “When any one of you has prayed two rak’ahs of Fajr, let him lie down on his right side.” (Narrated by Abu Dawood and al-Tirmidhi with an isnaad which is saheeh according to the conditions of al-Bukhaari and Muslim. Al-Tirmidhi said it is a saheeh hasan hadeeth).

Aishah says: “After the Prophet had prayed the two [sunnah] rak’at of the fajr, he would lie down on his right side.”

BismillahirRahmanirRahim
When ye have performed the prayers, remember Allah, standing, sitting down, or lying down on your sides;
(Al-Nisa 4:103)