All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
The Hadeeth (narration) which you referred to in the question is Saheeh [authentic] at the highest degree of authenticity as both Al-Bukhari and Muslim reported it.
Umm Hani said,
“I went to the Prophet on the day of the conquest of Makkah and I found him performing Ghusl (ritual bath), and his daughter Faatimah was screening him. I greeted him and he asked: "Who is that?" I said, "I, Umm Hani bint Abu Taalib." He said: "Welcome, O Umm Hani." When he had finished his Ghusl, he stood up and offered eight Rak’ahs (units of prayer) while dressed in one garment. When had finished his prayer, I said, "O Prophet of Allaah! My brother has declared that he will kill a man to whom I have granted asylum. The man is so and so Ibn Hubayrah." Then the Prophet said: ''O Umm Hani! We will grant asylum to the one whom you have granted asylum."
Umm Hani said, "That (visit) took place in the forenoon.” [Al-Bukhari and Muslim]
This Hadeeth was also reported in an abbreviated form by Imaam Maalik in Al-Muwatta’ and by Abu Daawood in his Sunan, and by Ahmad in his Musnad, and by Al-Haakim in his Mustadrak, and by Ibn Hibbaan in his Saheeh, and by Ibn Abu Shaybah, Abdur-Razzaaq and An-Nasaa’i in As-Sunan Al-Kubra .
Allaah Knows best.