Sahih Muslim Book 7, Hadith Number 2968.

Chapter : It is excellent that the aged and the weak, especially among the women, should hasten from Muzdalifa to Mina at the latter part of the night before the people moving in multitude. and excellence of staying there for others until they observe the dawn prayer at Muzdalifa.

‘Ata’ reported from Ibn Abbas (Allah be pleased with them): Allah’s Messenger (may peace be upon him) sent me from Muzdalifa along with his luggage (in the very early part of the dawn). I (Ibn Juraij, one of the narrators) said (to ‘Ati’): Has this (news) reached you that Ibn ‘Abbas (Allah be pleased with them) had said: “He (Allah’s Messenger) had sent me in the latter p4art of the night”?Thereupon he said: No, it was the dawn. I (again) said to him: (Did you hear) Ibn ‘Abbas (Allah be pleased with them) having said this (too): “We stoned al-Jamra before the dawn prayer”? So where did he observe the dawn prayer? He said: No. But he said only so much (as described above).