  It is shown that if the momenta belong to an integral lattice, then every
physical state of string theory leads to a symmetry of the scattering
amplitudes. We discuss the role of this symmetry when the momenta are those
provided by the usual D.D.F construction and show that the string compactified
on the torus associated with the self-dual Lorentzian lattice, $\Pi^{25,1}$
possess the Fake Monster Lie algebra as a symmetry.
