The Lunar Polar Hydrogen Mapper (LunaH-Map) is a cubesat mission designed to orbit the Moon and determine the amount of water ice in the permanently shadowed lunar polar craters. Its primary science objective is to use a miniaturized neutron spectrometer to count epithermal neutrons and map water abundance in the south polar permanently shadowed regions from low altitude (8-25 km) at resolution better than 20 square km. It is scheduled to launch on the Space Launch System Block 1 on the Artemis 1 mission in 2022.