His Hajj is valid, so he has done the Hajj that is required of him, but it will not be fully rewarded, rather the reward is greatly reduced.
Al-Nawawi said in al-Majmoo’ (7/62): If he does Hajj with haram money then he is sinning although his Hajj is valid and he has discharged his duty. This is the view of most of the fuqaha’.
In al-Mawsoo’ah al-Fiqhiyyah (17/131) it says:
If he does Hajj with dubious money or with money that was seized by force, his Hajj is valid according to the apparent meaning of the ruling, but he is a sinner and his Hajj is not fully rewarded. This is the view of al-Shafa’i, Malik and Abu Haneefah (may Allah have mercy on them) and of the majority of scholars of the earlier and later generations. Ahmad ibn Hanbal said: His Hajj is not valid if it is done with haram wealth. According to another report: it is valid but is haram. In a saheeh hadeeth it says that the Prophet (peace and blessings of Allah be upon him) mentioned a man who travels a long distance, with his hair disheveled, who stretches forth his hands to the heavens and says, ‘O Lord, O Lord,’ but his food is haram, his drink is haram, his clothes are haram, he is nourished with haram so how can he receive a response?
Shaykh Ibn Baz said:
His Hajj is valid if he does it as prescribed by Allah, but he is sinning because he took haram earnings. He has to repent to Allah from that and his Hajj is regarded as falling short because of that haram income, but he has discharged the obligation of Hajj.
Fatawa Ibn Baz, 16/387.
In Fatawa al-Lajnah al-Da’imah (11/43) it says that if Hajj is done with haram money that does not mean that the Hajj is not valid, but the person is sinning because he acquired haram wealth but that detract from the reward of Hajj or invalidate the Hajj.