  The algebras of the symmetry operators for the Hamilton-Jacobi and
Klein-Gordon-Fock equations are found for a charged test particle moving in an
external electromagnetic field in a spacetime manifold, on the isotropic (null)
hypersurface of which a three-parameter groups of motions act transitively.on
the isotropic (null) hypersurface of which a three-parameter groups of motions
act transitively. We have found all admissible electromagnetic fields for which
such algebras exist. We have proved that an admissible field does not deform
the algebra of symmetry operators for the free Hamilton-Jacobi and
Klein-Gordon-Fock equations. The results complete the classification of
admissible electromagnetic fields in which the Hamilton-Jacobi and
Klein-Gordon-Fock equations admit algebras of motion integrals that are
isomorphic to the algebras of operators of $r$-parametric groups of motions of
spacetime manifolds if $(r \leq 4)$.
