San Gabriel Mountains Protection Act This bill designates wilderness areas and wild and scenic rivers in California and modifies the boundaries of the San Gabriel Mountains National Monument in California to include additional National Forest System (NFS) land. Specifically, the monument shall include approximately 109,167 acres of additional NFS land. The bill designates parcels of NFS land as wilderness and components of the National Wilderness Preservation System to create the Condor Peak Wilderness and Yerba Buena Wilderness and to add to the San Gabriel Wilderness and Sheep Mountain Wilderness. The bill designates specified wild and scenic rivers. The Department of Agriculture may issue a special use authorization to the owners of a water transport or diversion facility located on NFS land in the Pleasant View Ridge Wilderness for the continued operation, maintenance, and reconstruction of the facility if specified conditions are met.