One may begin to fast even after having intimacy

I heard Abu Huraira (Allah be pleased with him) narrating that he who is overtaken by dawn in a state of seminal emission should not observe fast. I made a mention of it to 'Abd al-Rahman b. Harith (i. e. to his father) but he denied it. 'Abd al-Rahman went and I also went along with him till we came to'A'isha and Umm Salama (Allah be pleased with both of them) and Abd al-Rahman asked them about it.

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.  

كَانَ النَّبِيُّ ﷺ يُصْبِحُ جُنُبًا مِنْ غَيْرِ حُلُمٍ ثُمَّ يَصُومُ  

The dawn broke upon the Messenger of Allah ﷺ during the Ramadan in a state of junub not because of sexual dream (but on account of intercourse) and he washed himself and observed fast.  

أَنَّ عَائِشَةَ زَوْجَ النَّبِيِّ ﷺ قَالَتْ قَدْ كَانَ رَسُولُ اللَّهِ ﷺ يُدْرِكُهُ الْفَجْرُ فِي رَمَضَانَ وَهُوَ جُنُبٌ مِنْ غَيْرِ حُلُمٍ فَيَغْتَسِلُ وَيَصُومُ  

Abu Bakr reported that Marwan sent him to Umm Salama to ask whether a person should observe fast who is in a state of junub and the dawn breaks upon him, whereupon she said that the Messenger of Allah ﷺ (was at times) junbi on account of intercourse and not due to sexual dream, and the dawn broke upon him, but he neither broke the fast nor recompensed.  

أَنَّ مَرْوَانَ أَرْسَلَهُ إِلَى أُمِّ سَلَمَةَ ؓ يَسْأَلُ عَنِ الرَّجُلِ يُصْبِحُ جُنُبًا أَيَصُومُ فَقَالَتْ كَانَ رَسُولُ اللَّهِ ﷺ يُصْبِحُ جُنُبًا مِنْ جِمَاعٍ لاَ مِنْ حُلُمٍ ثُمَّ لاَ يُفْطِرُ وَلاَ يَقْضِي  

The Messenger of Allah ﷺ at times got up in the morning in a state of junub on account of having a sexual intercourse (with his wives during night) but not due to sexual dreams in the month of Ramadan, and would observe fast.  

عَنْ عَائِشَةَ وَأُمِّ سَلَمَةَ زَوْجَىِ النَّبِيِّ ﷺ أَنَّهُمَا قَالَتَا إِنْ كَانَ رَسُولُ اللَّهِ ﷺ لَيُصْبِحُ جُنُبًا مِنْ جِمَاعٍ غَيْرِ احْتِلاَمٍ فِي رَمَضَانَ ثُمَّ يَصُومُ  

Messenger of Allah, (the time) of prayer overtakes me as I am in a state of junub; should I observe fast (in this state)? Upon this the Messenger of Allah ﷺ said: (At times the time) of prayer overtakes me while I am in a state of junub, and I observe fast (in that very state), whereupon he said: Messenger of Allah, you are not like us Allah has pardoned all your sins, the previous ones and the later ones. Upon this he (the Holy Prophet) said: By Allah, I hope I am the most God-fearirg of you, and possess the best knowledge among you of those (things) against which I should guard.  

أَنَّ رَجُلاً جَاءَ إِلَى النَّبِيِّ ﷺ يَسْتَفْتِيهِ وَهِيَ تَسْمَعُ مِنْ وَرَاءِ الْبَابِ فَقَالَ يَا رَسُولَ اللَّهِ تُدْرِكُنِي الصَّلاَةُ وَأَنَا جُنُبٌ أَفَأَصُومُ فَقَالَ رَسُولُ اللَّهِ ﷺ وَأَنَا تُدْرِكُنِي الصَّلاَةُ وَأَنَا جُنُبٌ فَأَصُومُ فَقَالَ لَسْتَ مِثْلَنَا يَا رَسُولَ اللَّهِ قَدْ غَفَرَ اللَّهُ لَكَ مَا تَقَدَّمَ مِنْ ذَنْبِكَ وَمَا تَأَخَّرَ فَقَالَ وَاللَّهِ إِنِّي لأَرْجُو أَنْ أَكُونَ أَخْشَاكُمْ لِلَّهِ وَأَعْلَمَكُمْ بِمَا أَتَّقِي  

The Messenger of Allah ﷺ (at times) got up in the morning in a state of junub, not because of sexual dreams (but on account of intercourse at night), and then observed fast.  

أَنَّهُ سَأَلَ أُمَّ سَلَمَةَ ؓ عَنِ الرَّجُلِ يُصْبِحُ جُنُبًا أَيَصُومُ قَالَتْ كَانَ رَسُولُ اللَّهِ ﷺ يُصْبِحُ جُنُبًا مِنْ غَيْرِ احْتِلاَمٍ ثُمَّ يَصُومُ