Opioid Prescription Verification Act of 2019 This bill requires the Department of Health and Human Services, in consultation with relevant agencies, to update pharmacist training materials to include information about how to verify the identity of individuals who pick up prescribed medications; it also permits the Centers for Disease Control and Prevention to give preference, in awarding grants to states for overdose prevention, to states that maintain a prescription drug monitoring program and require dispensers of certain controlled substances to verify the identity of individuals who pick up prescribed medications.