Public Land Search and Rescue Act of 2022 This bill directs the Department of Justice (DOJ) to establish a program to allocate resources to remote search and rescue activities conducted on lands under the jurisdiction of the Department of Agriculture or the Department of the Interior. DOJ may award a grant under the program to a state or a political subdivision to (1) purchase equipment and gear necessary for remote search and rescue activities, (2) reimburse such an eligible recipient for the cost of maintenance and repair of remote search and rescue equipment owned or leased by the recipient, and (3) reimburse state and local agencies responsible for remote search and rescue activities. DOJ must prioritize an application from an eligible recipient who serves an area with a high ratio of visitors to residents. The federal share of assistance under the program shall be 75% of the cost of an eligible project.