The Book of Pilgrimage
وَحَدَّثَنَا أَبُو كَامِلٍ الْجَحْدَرِيُّ، حَدَّثَنَا سُلَيْمُ بْنُ أَخْضَرَ، حَدَّثَنَا عُبَيْدُ اللَّهِ بْنُ عُمَرَ، عَنْ نَافِعٍ، أَنَّ ابْنَ عُمَرَ، رَمَلَ مِنَ الْحَجَرِ إِلَى الْحَجَرِ وَذَكَرَ أَنَّ رَسُولَ اللَّهِ صلى الله عليه وسلم فَعَلَهُ .Nafi' reported that Ibn Umar (Allah he pleased with them) walked swiftly from stone to stone, and stated that Allah's Messenger (ﷺ) did like this
From Sahih Muslim, whose reports the scholars accept as authentic.