Authorizing Critical Conservation and Enabling Sportsmen and Sportswomen Act or the ACCESS Act This bill revises, reauthorizes, and establishes programs and entities regarding the conservation of wildlife and expanded access to hunting, fishing, and recreational shooting on federal lands. The bill makes permanent the authorizations for: (1) the program for the sale and exchange of public lands identified for disposal under approved land use plans, and (2) the Land and Water Conservation Fund. The bill revises requirements for appointment to the Board of Directors of the National Fish and Wildlife Foundation and reauthorizes the foundation through FY2022. This bill reauthorizes through FY2022 the Partners for Fish and Wildlife Program and the multinational species conservation funds. The Department of the Interior shall convene a panel of experts on great apes to identify the greatest needs and priorities for their conservation. Certain federal departments and agencies shall implement activities to protect water and wildlife to control invasive species on the lands which they manage. The bill establishes Theodore Roosevelt Genius Prize competitions regarding wildlife related concerns. The bill establishes the National Fish Habitat Board and provides for the designation of Fish Habitat Partnerships by it. Target Practice and Marksmanship Training Support Act The bill amends the Pittman-Robertson Wildlife Restoration Act to facilitate the construction and expansion of public target ranges. The bill declares that federal lands shall be open to hunting, fishing, and recreational shooting, unless closed in accordance with this bill.