Sunan Abi Dawud 1163
The above-mentioned tradition has also been transmitted by Muhammad b. Muslim through a different chain of narrators.  But there is no mention of prayer in this version. The version adds:
"He turned around his cloak, putting its right side on his left shoulder and its left side on his right shoulder.  Thereafter he made supplication to Allah."
حَدَّثَنَا مُحَمَّدُ بْنُ عَوْفٍ، قَالَ قَرَأْتُ فِي كِتَابِ عَمْرِو بْنِ الْحَارِثِ - يَعْنِي الْحِمْصِيَّ - عَنْ عَبْدِ اللَّهِ بْنِ سَالِمٍ، عَنِ الزُّبَيْدِيِّ، عَنْ مُحَمَّدِ بْنِ مُسْلِمٍ، بِهَذَا الْحَدِيثِ بِإِسْنَادِهِ لَمْ يَذْكُرِ الصَّلاَةَ قَالَ وَحَوَّلَ رِدَاءَهُ فَجَعَلَ عِطَافَهُ الأَيْمَنَ عَلَى عَاتِقِهِ الأَيْسَرِ وَجَعَلَ عِطَافَهُ الأَيْسَرَ عَلَى عَاتِقِهِ الأَيْمَنِ ثُمَّ دَعَا اللَّهَ عَزَّ وَجَلَّ ‏.‏