How did the Messenger of Allah (may Allah's peace and blessings be upon him) wash his head when he was in the state of Ihrām?

‘Abdullāh ibn ‘Abbās and Al-Miswar ibn Makhramah (may Allah be pleased with both of them) were debating whether the one in the state of Ihrām is allowed to wash his head or not. What made it debatable is that if one moves the hair on his head, it may cause some of the hair to fall. So ‘Abdullāh ibn Hunayn went to Abu Ayyūb and found him washing himself.

He said to Abu Ayyūb: Ibn ‘Abbās sent me to ask you how the Messenger of Allah (may Allah's peace and blessings be upon him) used to wash himself (while in Ihrām). Abu Ayyūb said to the one who was pouring the water for him: "Pour," after he had lowered the cloth that was screening him until his head was visible, then he moved his hair with his hands, going from back to front and from front to back.

Then he said: "This is what I saw the Messenger of Allah (may Allah's peace and blessings be upon him) doing." When ‘Abdullāh ibn Hunayn informed them (Ibn ‘Abbās and Al-Miswar) that ‘Abdullāh ibn ‘Abbās was right - as the Companions always sought to know what the correct thing to do is- Al-Miswar (may Allah be pleased with him) recanted and admitted the virtue of his companion, saying: "I will never argue with you again."