Is the committed son sinful because his father, who falsely claims to pray, does not pray?

You bear no sin for your father's abandonment of prayer, as long as you have forbidden him from the evil. The fundamental principle is to believe your father when he states that he prays, for prayer is a trust. However, if irrefutable evidence becomes clear to you that he does not pray, then continue to advise him gently and kindly, while observing proper etiquette.