We heard him say, "No one had more knowledge of the hadith of the Messenger of Allah ﷺ than I did, except for Abdullah bin Amr. He used to write them down with his hand and retain them in his heart, while I retained them in my heart but did not write them down with my hand. He sought permission from the Messenger of Allah ﷺ to write down what he heard from him, and he was granted permission."
حدثنا أحمد بن عبد الملك بن واقد الحراني قال حدثني محمد بن سلمة عن محمد بن إسحاق عن عمرو بن شعيب عن مجاهد والمغيرة بن حكيم
سمعناه يقول ما كان أحد أعلم بحديث رسول الله ﷺ مني إلا ما كان من عبد الله بن عمرو فإنه كان يكتب بيده ويعيه بقلبه وكنت أعيه بقلبي ولا أكتب بيدي واستأذن رسول الله ﷺ في الكتاب عنه فأذن له
Its chain of transmission is sahih. Bukhari related it in 1/29, in "Knowledge," in the chapter on writing down knowledge, with a slight difference in wording, and Tirmidhi related it in "Virtues," in the chapter on the virtues of Abu Hurairah, 5/661, no. 3841, where he said, hasan sahih, but he graded it daif in 5/40, no. 2668.