He told of a woman of Khath'am saying, “Messenger of God, God’s ordinance that His servants should perform the pilgrimage has come when my father is a very old man and is unable to sit firmly on a camel. May I perform the pilgrimage on his behalf?” He replied that she might. That was at the Farewell Pilgrimage.
Ibn ‘Abbas reported God’s messenger as saying, “An 'umra in Ramadan is equal to a hajja. ” (hajj is the word for the pilgrimage and hajja is a form indicating a single observance.)
He told of the Prophet meeting some riders at ar-Rauha’ (A place between thirty and forty miles from Medina on the way to Mecca) and asking who they were. They replied that they were Muslims and asked who he was. When he said that he was God's messenger a woman lifted up a boy to him and asked whether the child could be credited with having performed the pilgrimage, to which he replied, “Yes, and you will have a reward.”
He told of a man coming to the Prophet and saying that his sister had taken a vow to make the pilgrimage, but had died. The Prophet asked whether he would pay a debt, supposing she owed one, and when he replied that he would, he said, “Well, pay the debt due to God, for it is the one which most deserves to be paid.”
He reported God’s messenger as saying, “An 'umra is an expiation for sins committed between it and the next, but a hajj which is accepted will receive no less a reward than paradise.”