At-Tufail bin Ubayy bin Ka'b narrated from his father who said:
"When a third of the night had passed, the Messenger of Allah(s.a.w) stood and said: 'O you people! Remember Allah! Remember Allah! The Rajifah is coming, followed by the Radifah, death and what it brings is coming, death and what it brings is coming!'" Ubayy said: "I said: 'O Messenger of Allah! Indeed I say very much Salat for you. How much of my Salat should I make for you?' He said: 'As you wish.'" [He said:] "I said: 'A fourth?' He said: 'As you wish. But if you add more it would be better for you.' I said: 'Then half?' He said: 'As you wish. And if you add more it would be better [for you].'" [He said:] "I said: 'Then two-thirds? 'He said: 'As you wish, but if you add more it would be better for you.' I said: 'Should I make all of my Salat for you?' He said: 'Then your problems would be solved and your sins would be forgiven.'"
English reference: Vol. 4, Book 11, Hadith 2457
Arabic reference: Book 37, Hadith 2645