A hadith like this has been narrated by 'Abd al-Rahman b. al-Qasim with the same chain of transmitters.
Sahih Muslim Book 15, Hadith 325
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I wish I had sought permission from Allah's Messenger (ﷺ) as Sauda had sought, and observed the dawn prayer at Mina and stoned at al-Jamra before the people had come there. It was said to 'A'isha (Allah be pleased with her): Did Sauda seek permission from him (the Holy Prophet)? She said: Yes. She was a bulky lady and so she sought permission from Allah's Messenger (ﷺ) (to proceed to mina from Muzdalifa ahead of him), and he granted her permission.
Sahih Muslim Book 15, Hadith 324 Next Hadith → Asma' (Allah be pleased with her), as she was in the house at Muzdalifa, asked me whether the moon had set. I said: No. She prayed for some time, and again said: My son has the moon set? I said: Yes. And she said: Set forth along with me, and so we set forth until (we reached Mini) and the stoned at al-Jamra. She then prayed in her place. I said to her: Respected lady, we set forth (in the very early part of dawn) when it was dark, whereupon she said: My son, there is no harm in it; Allah's Apostle (ﷺ) had granted permission to women.
Sahih Muslim Book 15, Hadith 326
Sahih Muslim Book 15, Hadith 324 Next Hadith → Asma' (Allah be pleased with her), as she was in the house at Muzdalifa, asked me whether the moon had set. I said: No. She prayed for some time, and again said: My son has the moon set? I said: Yes. And she said: Set forth along with me, and so we set forth until (we reached Mini) and the stoned at al-Jamra. She then prayed in her place. I said to her: Respected lady, we set forth (in the very early part of dawn) when it was dark, whereupon she said: My son, there is no harm in it; Allah's Apostle (ﷺ) had granted permission to women.
Sahih Muslim Book 15, Hadith 326