Catalyzes the dephosphorylation of histidinol-phosphate to histidinol, the direct precursor of histidine. H2O + L-histidinol phosphate = L-histidinol + phosphate Amino-acid biosynthesis; L-histidine biosynthesis; L-histidine from 5-phospho-alpha-D-ribose 1-diphosphate: step 8/9. Cells lacking this gene exhibit an auxotrophy for histidine, but can grow on minimal medium supplemented with histidinol. Belongs to the inositol monophosphatase superfamily.