Strengthening Apprenticeships for Justice-Impacted Communities Act This bill supports pre-apprenticeships and apprenticeships, specifically regarding the justice-impacted population (i.e., individuals who have been arrested or convicted of a crime, including individuals currently or formerly incarcerated in a prison, jail, or juvenile facility). The Department of Labor may award grants to eligible applicants (i.e., local educational agencies, state registration agencies, and industries or businesses) to, among other things implement novel methods to improve pre-apprenticeship programs or apprenticeship programs available to incarcerated individuals, improve existing pre-apprenticeship programs and apprenticeship programs available to incarcerated individuals, and pilot novel approaches to provide apprenticeship training for justice-connected individuals that matches labor force needs. The bill establishes the Interagency Task Force on Strengthening Employment Opportunities and Outcomes for Justice-Impacted Communities that shall identify, evaluate, and make recommendations regarding (1) best practices relating to apprenticeship training for incarcerated individuals, and (2) ways in which federal agencies can better coordinate to support justice-impacted individuals with success and completion of pre-apprenticeships and apprenticeship programs. Labor shall establish an Office of Correctional Apprenticeships to ensure that all federal correctional institutions provide quality pre-apprenticeships and apprenticeship programs for incarcerated individuals that pay fair and graduated wages; be a nationwide repository for research, policies, and best practices in correctional education and training; and offer training and technical assistance for state prison systems and employers seeking to operate or improve corrections-based pre-apprenticeship or apprenticeship programs or pre-apprenticeship or apprenticeship programs that support justice-connected individuals.