I have also authenticated it in al-Ṣaḥīḥah, 2321.
He states: “2 – If a person performs a ghusl for janābah and has not yet made wuduʾ, the ghusl suffices for the wuduʾ. ʿĀʾishah said, ‘The Messenger of Allah ﷺ would not perform wuduʾ after the ghusl.’ It is likewise related from Ibn ʿUmar that, when a man told him, ‘I make wuduʾ after the ghusl,’ he replied, ‘You have gone to excess.’”
I say: this line of argument needs reconsideration. The report from Ibn ʿUmar is mawqūf and, even if sound, carries no binding proof. What the report apparently conveys—exactly as the hadith intends—is that the Sunnah is to perform wuduʾ before the ghusl, not after it. This is confirmed by her other narration in which she said:
“Whenever the Messenger of Allah ﷺ performed a ghusl after janābah, he would wash his hands, then perform the ablution he performed for prayer, and only thereafter take the ghusl …” — a hadith recorded by the Two Shaykhs and others.
There is no doubt that whoever performs wuduʾ both before and after the ghusl has lapsed into excess, whereas one who limits himself to wuduʾ only after the ghusl is acting contrary to the Sunnah. Thus ʿĀʾishah’s hadith does not state that the Prophet ﷺ omitted wuduʾ altogether during the ghusl; had it said so, the inference would have been correct—but since it does not, it is invalid.
The better proof is the hadith of Jābir ibn ʿAbd Allāh: the people of Ṭāʾif said, “O Messenger of Allah, our land is cold; what will suffice us for a ghusl after janābah?” He replied, “As for me, I pour water over my head three times.” Muslim and others transmitted it. Al-Bayhaqī cited this report for the issue, saying in his Sunan 1/177: “Chapter: Evidence that wuduʾ is subsumed within ghusl …” The import of the hadith is clear. When it is coupled with the report of ʿĀʾishah quoted by the author—authentic, as I have shown in Ṣaḥīḥ Sunan Abī Dāwūd, no. 244—the combined result is that the Prophet ﷺ would pray after a ghusl in which he had performed no wuduʾ, neither before nor after it. Allah knows best.