Mishkat al-Masabih 1140
‘A’isha said:
When God’s Messenger was seriously ill* and Bilal came to announce the time of prayer for him, he said, “Order Abu Bakr to lead the people in prayer.” So Abu Bakr led the prayer during those days, then when the Prophet experienced some improvement in his condition he got up and came into the mosque swaying between two men with his feet touching the ground. On hearing the sound Abu Bakr began to withdraw, but God’s Messenger signed to him not to do so. He then came and sat at Abu Bakr’s left, and Abu Bakr prayed standing and God’s Messenger prayed sitting, Abu Bakr following God’s Messenger’s prayer, while the people followed Abu Bakr’s. 

* Here the reference is to the Prophet's last illness.

(Bukhari and Muslim.) They both have a version which says that Abu Bakr caused the people to hear the takbir .
وَعَن عَائِشَة قَالَتْ: لَمَّا ثَقُلَ رَسُولَ اللَّهِ صَلَّى اللَّهُ عَلَيْهِ وَسَلَّمَ جَاءَ بِلَال يوذنه لصَلَاة فَقَالَ: «مُرُوا أَبَا بَكْرٍ أَنْ يُصَلِّيَ بِالنَّاسِ» فَصَلَّى أَبُو بَكْرٍ تِلْكَ الْأَيَّامَ ثُمَّ إِنَّ النَّبِيَّ صَلَّى اللَّهُ عَلَيْهِ وَسَلَّمَ وَجَدَ فِي نَفْسِهِ خِفَّةً فَقَامَ يُهَادَى بَيْنَ رَجُلَيْنِ وَرِجْلَاهُ يخطان فِي الْأَرْضِ حَتَّى دَخَلَ الْمَسْجِدَ فَلَمَّا سَمِعَ أَبُو بكر حسه ذهب أخر فَأَوْمَأَ إِلَيْهِ رَسُولُ اللَّهِ صَلَّى اللَّهُ عَلَيْهِ وَسَلَّمَ أَن لَا يتَأَخَّر فجَاء حَتَّى يجلس عَن يسَار أبي بكر فَكَانَ أَبُو بَكْرٍ يُصَلِّي قَائِمًا وَكَانَ رَسُولُ اللَّهِ صَلَّى اللَّهُ عَلَيْهِ وَسَلَّمَ يُصَلِّي قَاعِدًا يَقْتَدِي أَبُو بَكْرٍ بِصَلَاةِ رَسُولِ اللَّهِ صَلَّى اللَّهُ عَلَيْهِ وَسَلَّمَ وَالنَّاسُ مقتدون بِصَلَاة أبي بكر
وَفِي رِوَايَةٍ لَهُمَا: يُسْمِعُ أَبُو بَكْرٍ النَّاسَ التَّكْبِير