A man passed away without performing the obligatory hajj during his lifetime, so one of his sisters performed it on his behalf from her own money. Is this permissible?

 

Hajj is one of the pillars of Islam
God Almighty says, "And [due] to God from the people is a pilgrimage to the House-for whoever is able to find thereto a way” (Quran 3:97).

The Prophet (peace and blessings be upon him) said, "Islam is based on five things: Testifying that there is no deity save God and that Mohammed is His Messenger, performing prayers, giving zakat, making hajj, and fasting [the month of] Ramadan" (Bukhari and Muslim).

Among the conditions for the obligatoriness of hajj is the ability to undertake it as God mentions in the Quran and the Prophet (peace and blessings be upon him) in the Sunnah. Because ability is not only restricted to financial means but also includes a person's physical ability and safe journey among others, the Prophet (peace and blessings be upon him) said, "Whoever refrains from making hajj while he has provisions and safe means for traveling will die as a Christian or Jew" (Al-Tirmidhi).

Hajj, which is obligatory, is among the acts of worship that may be executed in another's stead. Amr Ibn Aws narrated from Abu Razin al-'Uqali that he approached the Prophet (peace and blessings be upon him) and said, 'O Messenger of God! My father is an old man and cannot make hajj, ‘umrah or travel." The Prophet (peace and blessings be upon him) replied, 'Make hajj and ‘umrah on behalf of your father'" (Al-Tirmidhi and Abu Dawud).

Conditions for making hajj in another’s stead
A person who makes hajj on behalf of another must have previously made his own obligatory hajj. Ibn Abbas narrated that the Prophet (peace and blessings be upon him) heard a man say, "O God! Here I am in response to Your call on behalf of Shubruma." He asked him, "Who is Shubruma?" The man replied, "A brother or close relative." The Prophet (peace and blessings be upon him) then asked him, "Have you made your own hajj?" The man replied in the negative, whereupon the Prophet (peace and blessings be upon him) said, "Perform your own hajj first and then make hajj on behalf of Shubruma" (Al-Tirmidhi).

The ruling
The hajj, which the sister of the deceased made out of her own expenses on behalf of her brother, is permissible and he will receive its reward by the will of God.

And God Almighty knows best.