This tradition has also been narrated through a different chain of transmitters by Umm Waraqah daughter of ‘Abd Allah b. al-Harith. The first version is complete. This version goes:
The Messenger of Allahﷺ used to visit her at her house. He appointed a mu’adhdhin to call adhan for her; and he commanded her to lead the inmates of her house in prayer. ‘Abd al-Rahman said: I saw her mu’adhdhin who was an old man.

حَدَّثَنَا الْحَسَنُ بْنُ حَمَّادٍ الْحَضْرَمِيُّ، حَدَّثَنَا مُحَمَّدُ بْنُ فُضَيْلٍ، عَنِ الْوَلِيدِ بْنِ جُمَيْعٍ، عَنْ عَبْدِ الرَّحْمَنِ بْنِ خَلاَّدٍ، عَنْ أُمِّ وَرَقَةَ بِنْتِ عَبْدِ اللَّهِ بْنِ الْحَارِثِ، بِهَذَا الْحَدِيثِ وَالأَوَّلُ أَتَمُّ قَالَ وَكَانَ رَسُولُ اللَّهِ ﷺ يَزُورُهَا فِي بَيْتِهَا وَجَعَلَ لَهَا مُؤَذِّنًا يُؤَذِّنُ لَهَا وَأَمَرَهَا أَنْ تَؤُمَّ أَهْلَ دَارِهَا . قَالَ عَبْدُ الرَّحْمَنِ فَأَنَا رَأَيْتُ مُؤَذِّنَهَا شَيْخًا كَبِيرًا .