Abdullah bin Abbas reported,

The Messenger of Allah ﷺ intended to perform Hajj, and a woman said to her husband, "Take me on Hajj with the Messenger of Allah on your camel."He said, "I have nothing on which to take you for Hajj."She said, "Take me on Hajj on your camel, such-and-such."He replied, "That one is reserved for the cause of Allah ."So he came to the Messenger of Allah ﷺ and said, "My wife sends you greetings of peace and the mercy of Allah. She has asked me to take her on Hajj with you. She said, 'Take me with the Messenger of Allah ﷺ,' and I said, 'I have nothing on which to take you for Hajj.' She said, 'Take me on your camel, such-and-such,' and I said, 'That one is reserved for the cause of Allah.'"The Messenger of Allah ﷺ said, "If you had taken her on Hajj on that camel, it would have been in the cause of Allah."The man continued, "She also asked me to inquire what is equivalent to performing Hajj with you."The Messenger of Allah ﷺ said, "Convey to her greetings of peace, the mercy of Allah, and His blessings, and inform her that it is equal to performing Hajj with me," meaning an Amra during Ramadan.

عن ابن عباس، قال

أراد رسول الله ﷺ الحج، فقالت امرأة لزوجها: أحجني مع رسول الله على جملك. فقال: ما عندي ما أحبك عليه. قالت: أحجني على جملك فلان. قال: ذاك حبيس في سبيل الله عز وجل. فأتى رسول الله ﷺ فقال: إن امرأتي تقرأ عليك السلام ورحمة الله، وإنها سألتني الحج معك، قالت: أحبني مع رسول الله ﷺ، فقلت: ما عندي ما أحجك عليه، فقالت: أحجني على جملك فلان، فقلت: ذاك حبيس في سبيل الله، فقال: أما إنك لو أحججتها عليه كان ذلك في سبيل الله قال: وإنها أمرتني أن أسألك ما يعدل حجة معك، فقال رسول الله ﷺ: اقرأها السلام ورحمة الله وبركاته، وأخبرها أنها تعدل حجة معي يعني عمرة في رمضان.