First written source in Isnad

In hadith collections, the isnad is quoted starting from the last in chain back to the first, e.g. حَدَّثَنَا عَبْدُ اللَّهِ بْنُ يُوسُفَ، قَالَ أَخْبَرَنَا مَالِكٌ، عَنْ هِشَامِ بْنِ عُرْوَةَ، عَنْ أَبِيهِ، عَنْ عَائِشَةَ Abdullah bin Yusuf related from Malik, from Hisham bin Aroua, from his father, from Aisha In this chain, the hadith was first passed down by word of mouth, and then written down. My question: In particular in the practice of Bukhari and Muslim, is the last in chain (in the example Abdullah bin Yusuf) always the first who has written down the hadit or does the chain include written collections/pre-collections? If the isnad contains written transmission, is it known by whom the hadith was first written down? ---------- Related questions: https://islam.stackexchange.com/questions/24469/how-can-one-check-isnad https://islam.stackexchange.com/questions/49967/how-can-scholars-of-jarh-and-taadil-be-certain-about-the-identity-of-a-narrator