a male maḥram who is willing to accompany her on the journey for Hajj?

Mālik and al-Shāfiʿī maintain that this is not a pre-condition for the obligation; a woman may set out for Hajj whenever she finds trustworthy company.

Abū Ḥanīfah, Aḥmad, and a number of other jurists hold that the presence—and consent—of a maḥram is a requisite for the duty to take effect.

The root of the disagreement lies in the apparent conflict between the general command to perform Hajj and to travel for it, and the Prophet’s prohibition against a woman travelling a journey of three days without a maḥram. It is authentically reported from him—may Allah bless him and grant him peace—through Abū Saʿīd al-Khudrī, Abū Hurayrah, Ibn ʿAbbās, and Ibn ʿUmar that he said:
“It is not lawful for a woman who believes in Allah and the Last Day to travel except with a maḥram.”

Hence, those who give precedence to the unrestricted command say: she may travel for Hajj even if no maḥram accompanies her. Those who restrict the general command by this ḥadīth, or who see the ḥadīth as defining the condition of “ability,” reply: she may not travel for Hajj unless a maḥram goes with her.

Thus we have spoken of the obligation of this rite—Hajj—what makes it obligatory, upon whom it is incumbent, and when it falls due.

What remains in this chapter is the ruling on the rite of ʿumrah. A group of scholars say it is obligatory; this is the position of al-Shāfiʿī, Aḥmad, Abū Thawr, Abū ʿUbayd, al-Thawrī, and al-Awzāʿī, and it is likewise reported from the Companions Ibn ʿAbbās and Ibn ʿUmar, as well as a number of the Followers.

Mālik and others regard it as a Sunnah.

Abū Ḥanīfah considers it supererogatory, and the same is related from Abū Thawr and Dāwūd. Those who deem it obligatory cite the Divine statement:
“Complete the Hajj and the ʿumrah for Allah” (Q 2:196),

along with several transmitted reports, among them the narration from Ibn ʿUmar, from his father, who said:

“A handsome Bedouin, dressed in white garments, entered upon the Messenger of Allah—may Allah bless him and grant him peace—and asked: ‘O Messenger of Allah, what is Islam?’ He replied: ‘To testify that there is no god but Allah and that Muhammad is the Messenger of Allah; to establish the prayer; to give the prescribed alms; to fast the month of Ramaḍān; to perform Hajj and ʿumrah; and to bathe after major impurity.’”

ʿAbd al-Razzāq relates that Maʿmar narrated from Qatādah that he used to recount: “When the verse, ‘And it is for Allah, upon people, to perform the pilgrimage to the House—whoever is able to find thereto a way’ (Q 3:97) was revealed, the Messenger of Allah—may Allah bless him and grant him peace—said: ‘It consists of two rites: Hajj and ʿumrah; whoever performs them both has fulfilled the obligation.’”

It is also narrated from Zayd ibn Thābit that he—may Allah bless him and grant him peace—said:
“Hajj and ʿumrah are two obligatory rites; it does not harm you which of them you begin with.”

And Ibn ʿAbbās said: “ʿUmrah is obligatory”—some transmit this statement ascribed directly to the Prophet—may Allah bless him and grant him peace.