كتاب الصيام
13  
The Book of Fasting
(26)
Chapter: It is Permissible to delay making up missed Ramadan Fasts until before the next Ramadan comes, and this is for those who broke the fast for a reason such as sickness, travel, menstruation and the like
(26)
باب قَضَاءِ رَمَضَانَ فِي شَعْبَانَ ‏
Sahih Muslim 1146 d

This hadith is reported on the authority of Yahya with the same chain of transmitters but no mention is made of the duty to the Messenger of Allah (ﷺ).

وَحَدَّثَنَا مُحَمَّدُ بْنُ الْمُثَنَّى، حَدَّثَنَا عَبْدُ الْوَهَّابِ، ح وَحَدَّثَنَا عَمْرٌو النَّاقِدُ، حَدَّثَنَا سُفْيَانُ، كِلاَهُمَا عَنْ يَحْيَى، بِهَذَا الإِسْنَادِ وَلَمْ يَذْكُرَا فِي الْحَدِيثِ الشُّغْلُ بِرَسُولِ اللَّهِ صلى الله عليه وسلم ‏.‏
Reference : Sahih Muslim 1146d
In-book reference : Book 13, Hadith 196
USC-MSA web (English) reference : Book 6, Hadith 2551
  (deprecated numbering scheme)