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 Activity is not influenced by the addition of S-adenosylmethionine, the allosteric activator of TS from Arabidopsis thaliana. Optimum pH is 9.5-10.5. Is inactive at pH values of 7 or less. Loses less than 10% of the initial activity during a 10 minutes incubation at 65 degrees Celsius. At 80 degrees Celsius, 90% of the activity is lost over the same time period. Amino-acid biosynthesis; L-threonine biosynthesis; L-threonine from L-aspartate: step 5/5. Homodimer. Was identified as a high-confidence drug target. Belongs to the threonine synthase family.