  The accuracy of the forward scattering approximation for two-point Green's
functions of the Anderson localization model on the Cayley tree is studied. A
relationship between the moments of the Green's function and the largest
eigenvalue of the linearized transfer-matrix equation is proved in the
framework of the supersymmetric functional-integral method. The new
large-disorder approximation for this eigenvalue is derived and its accuracy is
established. Using this approximation the probability distribution of the
two-point Green's function is found and compared with that in the forward
scattering approximation (FSA). It is shown that FSA overestimates the role of
resonances and thus the probability for the Green's function to be
significantly larger than its typical value. The error of FSA increases with
increasing the distance between points in a two-point Green's function.
