Is the الحج of a child below puberty valid?

A child's الحج is valid as a voluntary act of worship (nafl), but it does not fulfill the obligation of the الحج of Islam. When the child reaches puberty, they must perform the واجب الحج again. This is based on the hadith of Ibn Abbas: 'A woman lifted a child and asked: Is there الحج for this one? النبي (صلى الله عليه وسلم) said: Yes, and you will have a reward' (صحيح مسلم 1336). الشيخ ابن باز stated: 'The الحج of a child is valid as nafl but does not count as the واجب الحج' (Fatawa ابن باز, vol. 16).