Therapeutic Fraud Prevention Act of 2016 This bill prohibits sexual orientation or gender identity conversion therapy from being provided in exchange for monetary compensation. It bars advertisements for such therapy that claim to: (1) change an individual's sexual orientation or gender identity, (2) eliminate or reduce sexual or romantic attractions or feelings toward individuals of the same gender, or (3) be harmless or without risk. These prohibitions are inapplicable to practices or treatments that do not seek to change sexual orientation or gender identity if they provide: (1) assistance to an individual undergoing a gender transition; or (2) acceptance, support, and understanding of clients or facilitation of clients' coping, social support, and identity exploration and development, including sexual orientation-neutral interventions to prevent or address unlawful conduct or unsafe sexual practices. The Federal Trade Commission and states are provided authority to enforce against violations.