Proxy الحج (الحج al-badal) has specific conditions that must be fulfilled for it to be valid. All four schools agree on the core requirements, with some variation in details. The fundamental conditions are agreed upon by the scholars based on the hadith evidence.
الشيخ ابن باز outlined the conditions as follows: First, the proxy must be a Muslim of sound mind and must have reached puberty. Second, the proxy must have already performed their own واجب الحج before performing الحج for someone else — this is based on the hadith of Shubrumah. Third, the person on whose behalf الحج is performed must be either deceased or permanently unable to perform الحج due to old age or incurable illness. Temporary illness or temporary financial difficulty does not justify proxy الحج. Fourth, the proxy must make the intention (niyyah) at the الميقات specifically on behalf of the other person, saying 'Labbayk on behalf of [name].' Fifth, the proxy performs all the rites exactly as they would for their own الحج.
الشيخ ابن عثيمين added that the proxy should be someone known for their religiousness and trustworthiness, as they are performing a sacred act of worship. He also clarified that the proxy earns reward for their good deed, while the full reward of الحج goes to the person on whose behalf it is performed. If the proxy commits a violation during الحج that requires a penalty, they bear the penalty themselves, not the person on whose behalf they are performing الحج.