All perfect praise be to Allah, the Lord of the Worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and messenger.
When a person performs Hajj before making up for the missed fast-days of Ramadan, his Hajj is valid because clearing one's liability from the missed fast-days of Ramadan is not among the conditions for the validity of Hajj. There is no doubt that it is better for the person to hasten to make up for the missed fast-days. Allah, The Exalted, says (what means): {And hasten to forgiveness from your Lord and a garden as wide as the heavens and earth, prepared for the righteous.} [Quran 3:133]
Allah Knows best.