Monoterpene synthase that catalyzes the formation of (3R)-linalool from geranyl diphosphate. (2E)-geranyl diphosphate + H2O = (R)-linalool + diphosphate Binds 3 Mg(2+) or Mn(2+) ions per subunit. Secondary metabolite biosynthesis; terpenoid biosynthesis. The Asp-Asp-Xaa-Xaa-Asp/Glu (DDXXD/E) motif is important for the catalytic activity, presumably through binding to Mg(2+). Belongs to the terpene synthase family. Tpsb subfamily.