Caution: Translations of Quran and Ḥadīth may lead to possible misapplications and misinterpretations. This site is intended for students of sacred knowledge that are proficient in comprehending classical Arabic and have a strong foundation in Islamic sciences. Also note that religious injunctions rely on several aspects beyond what one may glean through reading individual aḥādīth.
bayhaqi:9384Abū Bakr Aḥmad b. al-Ḥasan al-Qāḍī > Abū al-ʿAbbās al-Aṣam > al-Rabīʿ > al-Shāfiʿī > Ibn ʿUyaynah > Ibn Ṭāwus from his father

[Machine] The messenger of Allah ﷺ commanded his companions to perform and fulfill the migration, and he spent the night with his wives on his riding camel, taking turns to hold the reins. I think he said he kissed the corner of the cloak. The Sheikh narrated that he rode between Safa and Marwa during Sa'y (the ritual of running between the two hills), and Allah knows best what he intended with his Sa'y after completing the first Tawaf (circumambulation around the Kaaba). As for after completing the Sa'y of I'tifadah (another type of Sa'y during Hajj), it is not preserved that he performed Sa'y between the two hills, and Allah knows best.  

البيهقي:٩٣٨٤وَذَكَرَ الْحَدِيثَ الْمُرْسَلَ الَّذِي 9384 أَخْبَرَنَاهُ أَبُو بَكْرٍ أَحْمَدُ بْنُ الْحَسَنِ الْقَاضِي ثنا أَبُو الْعَبَّاسِ الْأَصَمُّ أنبأ الرَّبِيعُ أنبأ الشَّافِعِيُّ أنبأ ابْنُ عُيَيْنَةَ عَنِ ابْنِ طَاوُسٍ عَنْ أَبِيهِ

أَنَّ رَسُولَ اللهِ ﷺ أَمَرَ أَصْحَابَهُ أَنْ يُهَجِّرُوا بِالْإِفَاضَةِ وَأَفَاضَ فِي نِسَائِهِ لَيْلًا عَلَى رَاحِلَتِهِ يَسْتَلِمُ الرُّكْنَ بِمِحْجَنِهِ أَحْسَبُهُ قَالَ وَيُقَبِّلُ طَرَفَ الْمِحْجَنِ قَالَ الشَّيْخُ وَالَّذِي رَوَى عَنْهُ أَنَّهُ طَافَ بَيْنَ الصَّفَا وَالْمَرْوَةِ رَاكِبًا فَإِنَّمَا أَرَادَ وَاللهُ أَعْلَمُ فِي سَعْيِهِ بَعْدَ طَوَافِ الْقُدُومِ فَأَمَّا بَعْدَ طَوَافِ الْإِفَاضَةِ فَلَمْ يُحْفَظْ عَنْهُ أَنَّهُ طَافَ بَيْنَهُمَا وَاللهُ أَعْلَمُ