Sayyiduna Abu Hurayrah (may Allah be pleased with him) narrates: The Prophet (peace and blessings be upon him) asked Sayyiduna Abu Bakr (may Allah be pleased with him); he said: When do you perform the witr? He replied: I perform the witr in the early part of the night. The Prophet (peace and blessings be upon him) said: This is the way of a cautious and sensible person. Then he asked Sayyiduna Umar (may Allah be pleased with him): When do you perform the witr? He replied: In the last part of the night. The Prophet (peace and blessings be upon him) said: This is the way of a strong person and one who has been given help.
Imam al-Bazzar and Imam al-Tabarani in al-Mu'jam al-Awsat recorded this narration; its chain contains a narrator, Sulayman bin Dawud al-Yamami, who is extremely da'if (weak).