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. When comparing gene expression levels of the four IMPase family genes in exponential cultures of M.tuberculosis, the level of cysQ is the highest, almost equal to sigA; impA and impC are expressed at approximately 40% of this level, while suhB is lowest, at 12% of the cysQ level. Strains lacking this gene appear to be not viable, even in the presence of high levels of exogenous inositol. Belongs to the inositol monophosphatase superfamily.