Nafi reported,

People say that Ibn Umar accepted Islam before Umar, but that is not the case. Rather, on the day of Hudaybiyyah, Umar sent Abdullah to fetch a horse of his that was with a man of the Ansar, so that he could ride it into battle. Meanwhile, the Messenger of Allah ﷺ was receiving the pledge of allegiance under the tree, and Umar did not know of it. Abdullah gave his pledge, then went to fetch the horse and brought it to Umar, who was putting on his armor for battle. He informed him that the Messenger of Allah ﷺ was taking the pledge under the tree.He said, so Umar set out and went with him until he gave his pledge to the Messenger of Allah ﷺ. This is what people are referring to when they say that Ibn Umar accepted Islam before Umar.

Azami 8989

Sahih

عن نافع قال

إن الناس يتحدثون أن ابن عمر أسلم قبل عمر، وليس كذلك، ولكن عمر يوم الحديبية أرسل عبد الله إلى فرس له عند رجل من الأنصار، يأتي به ليقاتل عليه، ورسول الله ﷺ يبايع عندالشجرة، وعمر لا يدري بذلك، فبايعه عبد الله ثم ذهب إلى الفرس، فجاء به إلى عمر وعمر، يستلئم للقتال، فأخبره أن رسول الله ﷺ يبايع تحت الشجرة، قال: فانطلق فذهب معه حتى بايع رسول الله ﷺ، فهمي التي يتحدث الناس أن ابن عمر أسلم قبل عمر.

الأعظمي 8989صحيح
Contents
Reference
Commentary
Ayat
Collection
Jami al-Kamil
Book
Biography of the Prophet ﷺ
Chapter
Expedition of Hudaybiya and expedition of Dhat al-Qarad
Section
Pledge of allegiance to Umar bin Khattab
Numbering
Jami al-Kamil 8989 (2nd edition)
Azami 8989