Justice and Mental Health Collaboration Reauthorization Act of 2022 This bill modifies and reauthorizes through FY2026 the Justice and Mental Health Collaboration Program. The program provides state, local, and tribal grants to improve the criminal justice system's response to people with mental health disorders. Among the modifications, the bill allows funds for diversion and alternative prosecution and sentencing programs to be used for training for state and local prosecutors related to diversion programs; allows funds for multidisciplinary teams to be used to support police officers and mental health crisis workers responding together to mental health calls; and allows grants to be awarded for additional purposes such as suicide prevention programs and services, case management services, and state and local implementation of the 988 suicide hotline. Additionally, the bill reauthorizes through FY2026 the requirement for the Department of Justice to examine and report on the prevalence of mentally ill offenders in prisons and jails.