What is hajj badal (hajj on someone's behalf)?

“Yes, it will be permissible. Since your father did not make a wasiyyat that hajj-e-badal be done from one third of his estate, the hajj which you will do will be a nafil hajj and will take place on your behalf. Thereafter, you should convey the reward of the nafil hajj to your father.”

“It is permissible to perform Hajj on behalf of a deceased person who has not performed Hajj during his lifetime. If the deceased person made a bequest (Wasiyyah) to perform hajj on his behalf, then the expenses of performing Hajj on his behalf would be paid from one third of his nett estate.”

“1. A menstruating female must perform Tawāf Al-Ziyārah whenever she becomes pure. Her Fardh Hajj is valid. 2. It is better for one who has already fulfilled his Fardh Hajj to perform Hajj on behalf of the deceased.”

“(1) When Hajj is performed on behalf of another person, it is called Hajj-e-Badal. (2) If Hajj was obligatory upon someone and he made a bequest (Wasiyyah), then Hajj-e-Badal should be done as Ifrād (single Hajj without ‘Umrah).”