Which type of Hajj is most suitable for the sick or deceased, on whose behalf the obligatory Hajj is performed: Qiran, Tamattu‘, or Ifrad, and why?

The original principle is that an agent is a trustee who acts in the best interest of his principal. The best course of action here is for him to perform the tamattu‘ pilgrimage on her behalf, based on the saying of Anas ibn Malik: "We set out proclaiming the Hajj, and when we arrived in Mecca, the Messenger of Allah, may Allah's peace and blessings be upon him, commanded us to make it an ‘Umrah." This is unless the principal stipulated a specific ritual for him, in which case he must adhere to the condition.