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 Allosterically activated by S-adenosyl-L-methionine (SAM). Activated by S-adenosyl-L-ethionine, 5'-amino-5'-deoxyadenosine, sinefungin and 5'-deoxy-5-methylthioadenosine. Inhibited by AMP. Amino-acid biosynthesis; L-threonine biosynthesis; L-threonine from L-aspartate: step 5/5. Homodimer. The N-terminal domain (1-77) is essential for regulation by S-adenosyl-L-methionine and AMP, but not for dimerization. Binds 4 S-adenosyl-L-methionine (SAM) molecules per dimer. Although SAM3 and SAM4 have equivalent positions, their interactions with the protein are not identical. SAM3 interacts with Lys-181 and Asn-187 of monomer B, whereas SAM4 interacts only with Lys-181 of monomer A. Much more active than TS2 at physiological concentrations of S-adenosyl-L-methionine (20 uM). Belongs to the threonine synthase family.