One may begin to fast even after having intimacy
Both of them said: (At times it so happened) that the Messenger of Allah ﷺ woke up in the morning in a state of junub (but without seminal emission in a dream) and observed fast.
He (the narrator) said: We then proceeded till we went to Marwan and Abd al-Rahman made a mention of it to him. Upon this Marwan said: I stress upon you (with an oath) that you better go to Abu Huraira and refer to him what is said about it. So we came to Abu Huraira and Abu Bakr had been with us throughout and 'Abd al-Rahman made a mention of it to him, whereupon Abu Huraira said: Did they (the two wives of the Holy Prophet) tell you this? He replied: Yes Upon this (Abu Huraira) said: They have better knowledge. Abu Huraira then attributed that what was said about it to Fadl b. 'Abbas and said: I heard it from Fadl and not from the Messenger of Allah ﷺ. Abu Huraira then retracted from what he used to say about it. Ibn Juraij (one of the narrators) reported: I asked 'Abd al-Malik, if they (the two wives) said (made the statement) in regard to Ramadan, whereupon he said: It was so, and he (the Holy Prophet) (woke up in the) morning in a state of junub which was not due to the wet dream and then observed fast.