Expressing the intention in various formulae does not affect the intention

A: If the situation is as you have mentioned, then performing Hajj on behalf of "Thalibah" and on behalf of "Halibah" is valid, and the forgetfulness of the one who performed Hajj on behalf of "Halibah" when erroneously making the intention to perform Hajj in the name of "Thalibah" does not jeopardize his performance of Hajj on behalf of "Halibah". The crucial factor is the intention of the one who paid the money when commissioning the person to perform Hajj on behalf of "Halibah", as (Part No. 10; Page No. 120) Prophet Muhammad (peace be upon him) said: Actions are judged by the intentions, and every person will be rewarded according to what he has intended. May Allah grant us success. May peace and blessings be upon our Prophet Muhammad, his family, and Companions.