Is the Hajj of a person who has not paid Zakat on part of his money for many years valid, knowing that he performed Hajj with this money and intended to pay Zakat after returning, and he acknowledges the obligation of Zakat?

Failing to pay Zakat (definition) does not affect the validity of Hajj, because performing Hajj with money that has the rights of others in it does not invalidate it. Rather, even if one performs Hajj with purely unlawful money, the Hajj is valid according to most scholars, though it is accompanied by sin. Zakat is one of the pillars of Islam and must be paid without delay.