Volcanic Ash and Fumes Act of 2022 This bill incorporates the capacities and expertise of the National Oceanic and Atmospheric Administration (NOAA) into the National Volcano Early Warning and Monitoring System. Specifically, the bill integrates into the purposes of the system relevant capacities of NOAA to strengthen the warning and monitoring systems of volcano observatories in the United States. This includes observations and modeling of the results from volcanic eruptions (e.g., emissions of gases, aerosols, and ash; atmospheric dynamics and chemistry; and ocean chemistry) that are carried out by NOAA's Volcanic Ash Advisory Centers located in Anchorage, Alaska, and the District of Columbia. The bill provides for a memorandum of understanding to establish cooperative support for the activities of the system from NOAA, including environmental observations, modeling, and temporary duty assignments of personnel to support emergency activities. The Department of Commerce must (1) submit to the U.S. Geological Survey (USGS) annual cost estimates for modernization activities and support of the system for NOAA; and (2) collaborate with the USGS to implement activities related to the expertise of NOAA, including observations and modeling of results from volcanic eruptions. Commerce must develop a plan to implement this bill during the five-year period beginning on the date on which the plan is developed. The plan shall include an estimate of the cost and schedule required for implementation. Upon the plan's completion, Commerce shall make it publicly available.