Strengthening Our Health Security Act of 2022 This bill requires the Department of Health and Human Services (HHS) to meet conditions related to notification and planning before terminating certain restrictions on imports and individuals entering the United States. Current law authorizes HHS to restrict entries and imports from foreign countries to prevent the introduction of communicable diseases. HHS exercised this authority as part of its COVID-19 response, including to allow for the expulsion of undocumented migrants at the border without any asylum processing. Under this bill, HHS may not terminate the restrictions for (1) at least 60 days after it notifies Congress of the end of the COVID-19 emergency, and (2) at least 30 days after it submits to Congress a plan for addressing the possible influx of migrants or imports resulting from lifting the restrictions.