  We study the super and dynamical symmetries of a fermion in a monopole
background. The Hamiltonian also involves an additional spin-orbit coupling
term, which is parameterized by the gyromagnetic ratio. We construct the
superinvariants associated with the system using a SUSY extension of a
previously proposed algorithm, based on Grassmann-valued Killing tensors.
Conserved quantities arise for certain definite values of the gyromagnetic
factor: $\N=1$ SUSY requires $g=2$; a Kepler-type dynamical symmetry only
arises, however, for the anomalous values $g=0$ and $g=4$. The two anomalous
systems can be unified into an $\N=2$ SUSY system built by doubling the number
of Grassmann variables. The planar system also exhibits an $\N=2$ supersymmetry
without Grassmann variable doubling.
