Professional's Access To Health Workforce Integration Act of 2022 This bill authorizes a grant program to assist unemployed and underemployed skilled immigrants who are internationally trained health professionals with entering the U.S. health workforce. The grants may be awarded by (1) the Bureau of Health Workforce within the Health Resources and Services Administration, (2) the National Institute on Minority Health and Health Disparities, or (3) the Office of Minority Health. Eligible grant recipients include clinical, public health, or health services organizations; community-based organizations; academic institutions; and states and localities.