Amr bin Abasa reported,
I asked, "Messenger of Allah, is there any hour closer to Allah than another? Is there any hour in which remembrance of Him is especially sought?"He replied, "Yes. The closest the Lord 
is to His servant is in the latter part of the night. If you can be among those who remember Allah in that hour, then do so, for prayer at that time is attended and witnessed by the angels until sunrise."
Azami 10929
Sahihعن عمرو بن عبسة يقول
قلت: يا رسول الله! هل من ساعة أقرب من الأخرى؟ أو هل من ساعة يبتغى ذكرها؟ قال: نعم، إن أقرب ما يكون الرب عز وجل من العبد جوف الليل الآخر، فإن استطعت أن تكون ممن يذكر الله عز وجل في تلك الساعة فكن، فإن الصلاة محضورة مشهودة إلى طلوع الشمس.
Nasai (572) narrated it from Amr bin Mansur, Adam bin Abu Iyas told us, Layth bin Saad told us, Muawiya bin Salih told us, he said, Abu Yahya Salim bin Amir, Damra bin Habib, and Abu Talha Nuaym bin Ziyad informed me, they said, We heard Abu Umama Bahili say, I heard Amr bin Abasa say, and then he narrated it.Tirmidhi (3579) also narrated it through Muawiya bin Salih, in shortened form, and said, "Hasan sahih gharib from this route." I say, it is as he said, for it is sahih, and Ibn Khuzayma (1147) and Hakim (1/409) both graded it sahih, both through this same route. Hakim said, "It meets the standard of Muslim."Abu Dawud (1277) narrated it through another route from Abu Umama, and it contains the question, "Which part of the night is most heard?" He replied, "The latter part of the deep night, so pray whatever you wish, for prayer at that time is witnessed and recorded."Abu Umama is Sudayy bin Ajlan Bahili, a well known companion, and the origin of this hadith is found in Sahih Muslim (832), in the account of the conversion of Amr bin Abasa to Islam.