Engaging in haram acts does not mean one abandons their devotion to Allah ta'ala and their 'ibadah.
Indeed, it is even more important to stress on that, for the purpose of hopefully empowering oneself to become more obedient to God and stay away from sin.
Yes, this man should continue to pray, fast, and perform everything else required by him as a Muslim. If done in the correct way, they will also be valid as well.
With prayers for your success.