Safer Prescribing of Controlled Substances Act This bill amends the Controlled Substances Act to require a practitioner (other than a hospital, pharmacy, or veterinarian) to complete training, as a condition of obtaining or renewing a registration to dispense or conduct research with controlled substances in schedule II, III, IV, or V. The training must meet certain requirements, including providing information on best practices for pain management and responsible prescribing of pain medications. The Substance Abuse and Mental Health Services Administration must establish a training module that meets the requirements.