Catalyzes the gamma-elimination of phosphate from L-phosphohomoserine and the beta-addition of water to produce L-threonine. To a lesser extent, is able to slowly catalyze the deamination of L-threonine into alpha-ketobutyrate and that of L-serine and 3-chloroalanine into pyruvate. Is also able to rapidly convert vinylglycine to threonine, which proves that the pyridoxal p-quinonoid of vinylglycine is an intermediate in the TS reaction. H2O + O-phospho-L-homoserine = L-threonine + phosphate Is competitively inhibited by L-threo-3-hydroxyhomoserine phosphate. Amino-acid biosynthesis; L-threonine biosynthesis; L-threonine from L-aspartate: step 5/5. Belongs to the threonine synthase family.