The Prophet ﷺ said, "If somebody eats or drinks forgetfully then he should complete his fast, for what he has eaten or drunk, has been given to him by Allah."  

عَنِ النَّبِيِّ ﷺ قَالَ إِذَا نَسِيَ فَأَكَلَ وَشَرِبَ فَلْيُتِمَّ صَوْمَهُ فَإِنَّمَا أَطْعَمَهُ اللَّهُ وَسَقَاهُ  

From his father who said: "I said. 'O Messenger of Allah! Inform me about Wudu.' So he said: "Perform Wudu well, and go between the fingers, and perform Istinshaq extensively except when fasting."  

قُلْتُ يَا رَسُولَ اللَّهِ أَخْبِرْنِي عَنِ الْوُضُوءِ قَالَ أَسْبِغِ الْوُضُوءَ وَخَلِّلْ بَيْنَ الأَصَابِعِ وَبَالِغْ فِي الاِسْتِنْشَاقِ إِلاَّ أَنْ تَكُونَ صَائِمًا  

At times Messenger of Allah ﷺ used to get up in the morning in the state of Janaba after having sexual relations with his wives. He would then take a bath and fast.  

أَنَّ رَسُولَ اللَّهِ ﷺ كَانَ يُدْرِكُهُ الْفَجْرُ وَهُوَ جُنُبٌ مِنْ أَهْلِهِ ثُمَّ يَغْتَسِلُ وَيَصُومُ  

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