Finish the Wall Act This bill requires the Department of Homeland Security (DHS) to resume activities related to the construction of a barrier system along the U.S.-Mexico border and addresses other border-related issues. DHS must resume all such construction activities that were planned or underway prior to January 20, 2021. DHS must also expend all funds appropriated or explicitly obligated since October 1, 2016, for construction of this barrier system. DHS may not cancel contracts for activities related to such construction entered into on or before January 20, 2021. Furthermore, within 14 days of this bill's enactment, DHS must certify to Congress that U.S. Customs and Border Protection facilities that process adults taken into custody at the border are fully compliant with certain laws related to the collection of DNA. (Among other things, these laws allow for the collection of DNA samples from non-U.S. persons detained under U.S. authority.)