Catalyzes the gamma-elimination of phosphate from L-phosphohomoserine and the beta-addition of water to produce L-threonine. H2O + O-phospho-L-homoserine = L-threonine + phosphate Amino-acid biosynthesis; L-threonine biosynthesis; L-threonine from L-aspartate: step 5/5. Homodimer. Belongs to the threonine synthase family.