Catalyzes the gamma-elimination of phosphate from L-phosphohomoserine and the beta-addition of water to produce L-threonine. Does not catalyze the conversion of O-acetyl-L-homoserine into threonine. H2O + O-phospho-L-homoserine = L-threonine + phosphate Amino-acid biosynthesis; L-threonine biosynthesis; L-threonine from L-aspartate: step 5/5. Homotrimer. The N-terminal 41 amino acids are required for activity. Belongs to the threonine synthase family.