All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
The conditions of the Hajj of women, particularly, include being accompanied by a Mahram (i.e. an unmarriageable relative), like a father, a brother, any other Mahram or the husband.
Therefore, if the woman meets the required conditions, including financial ability and the presence of a Mahram or a husband, but she did not perform Hajj without a Sharee‘ah approved excuse till she died, then it is obligatory to authorize someone to perform Hajj on her behalf, whether she commanded this in her will or not. The proof is the Hadeeth of Ibn ‘Abbaas in which a woman from the tribe of Juhaynah came to the Prophet, sallallaahu ‘alayhi wa sallam, and said: "My mother had vowed to perform Hajj but she died before performing it. May I perform Hajj on my mother's behalf?” The Prophet replied: “Yes, perform Hajj on her behalf.” [Al-Bukhari]
Al-Haafith Ibn Hajar said in Al-Fat-h upon explaining this Hadeeth: “This Hadeeth indicates that if someone dies while Hajj is due from him, then his guardian is liable to arrange someone to perform Hajj on behalf of the deceased from his property just as he is liable to repay his debts.” Note that the Mahram is not only a husband; rather, any Mahram through blood, suckling or marriage relationships suffices to make a woman’s travel permissible. Hajj becomes obligatory upon every woman who can financially afford Hajj and has a Mahram that can travel with her.
Allah Knows best.