The Rites of Hajj (Kitab Al-Manasik Wa'l-Hajj)
Dawud :: Book 10 : Hadith 1985
Narrated Abdullah Ibn Abbas:
The Apostle of Allah (peace_be_upon_him) intended to perform hajj.
A woman said to her husband: Let me perform hajj along with the Apostle of Allah (peace_be_upon_him).
He said: I have nothing on which I can let you perform hajj. She said: You may perform hajj on your such-and-such camel. He said: That is dedicated to the cause of Allah, the Exalted. He then came to the Apostle of Allah (peace_be_upon_him) and said: My wife has conveyed her greetings and the blessings of Allah to you. She has asked about performing hajj along with you. She said (to me): Let me perform hajj with the Apostle of Allah (peace_be_upon_him). I said (to her): I have nothing upon which I can let you perform hajj. She said: Let me perform hajj on your such-and-such camel. I said: That is dedicated to the cause of Allah, The Exalted.
He replied: If you let her perform hajj on it, that would be in the cause of Allah.
He said: She has also requested me to ask you: What is that action which is equivalent to performing hajj with you?
The Apostle of Allah (peace_be_upon_him) said: Convey my greetings, the mercy of Allah and His blessings to her and tell her that umrah during Ramadan is equivalent to performing hajj along with me.