If one willed that a Hajj is performed by proxy after his death...
If one willed that a Hajj is performed by proxy after his death, then it is mandatory to execute that will if the cost of the Hajj is not more than one third of what he has left behind, unless the inheritors agree to it, if it were to be more than one third. This is case if the Hajj is not obligatory upon the deceased (i.e. not his first Hajj).
However if it is obligatory upon the deceased, then the Hajj must be performed by proxy on behalf of the deceased in any way, even if the cost is more than one third. If one vowed, or promised Allah that he would go to Hajj, then he must do so even if he had performed Hajj before.
If before qualifying for, or being able to go to, Hajj, one vowed to be, say, in Karbala on the Day of ARAFAH, but afterwards he could meet the criteria to go to Hajj, then his/her vow is superseded, and he must go to Hajj. A man may go to Hajj on behalf of a woman, and vice versa. One may, in the mandatory Hajj, intend to do the Hajj on behalf of the , peace be upon him and his family, or the infallible Imam (pbuh), or anyone else, dead or alive.
The reward of the Hajj will be written for him and whomever he intended the Hajj for. It is desirable for one to go to Hajj every year, and the reward of the Hajj is greater than giving the cost of the Hajj to charity in the cause of Allah. If one is able do the Hajj without the Umrah, or to do the Umrah without the Hajj, then he must do whatever he is able to do.
If a woman started her period before the IHRAAM, and she declared her IHRAAM in that state, then if the monthly period ended and she became TAAHIR before the WUQUF in ARAFAAT, then it is obligatory upon her to do the duties of the Umrah of TAMATTU'. If she is not TAAHIR by the time of the WUQUF in ARAFAAT, then it is obligatory upon her to switch to the Hajj of al-EFRAAD. She then must perform WUQUF in ARAFAAT and the duties of Hajj of TAMATTU'.
[All the Hajj of TAMATTU' duties must be performed except the TAWAAF, SA'Y and associated SALA, which necessitates going to the Holy Mosque of the CA'BAH. {These correspond to Duties in Makkah, duties 7 - 11 of the 13 duties list of the Hajj of TAMATTU', given above.} When she is TAAHIR, she can continue to perform the remaining the duties of the Hajj of TAMATTU'.] After this she must do the MUFRADAH Umrah. The same ruling applies if either HAYDH or NIFAAS occurs after IHRAAM and before TAWAAF.