  We use the conditional symmetry approach to study the $r$-evolution of a
minisuperspace spherically symmetric model both at the classical and quantum
level. After integration of the coordinates $t$, $\theta$ and $\phi$ in the
gravitational plus electromagnetic action the configuration space dependent
dynamical variables turn out to correspond to the $r$-dependent metric
functions and the electrostatic field. In the context of the formalism for
constrained systems (Dirac - Bergmann, ADM) with respect to the radial
coordinate $r$, we set up a point-like reparameterization invariant Lagrangian.
It is seen that, in the constant potential parametrization of the lapse, the
corresponding minisuperspace is a Lorentzian three-dimensional flat manifold
which obviously admits six Killing vector fields plus a homothetic one. The
weakly vanishing $r$-Hamiltonian guarantees that the phase space quantities
associated to the six Killing fields are linear holonomic integrals of motion.
The homothetic field provides one more rheonomic integral of motion. These
seven integrals are shown to comprise the entire classical solution space, i.e.
the space-time of a Reissner-Nordstr\"om black hole, the $r$-reparametrization
invariance since one dependent variable remains unfixed, and the two quadratic
relations satisfied by the integration constants. We then quantize the model
using the quantum analogues of the classical conditional symmetries, and show
that the existence of such symmetries yields solutions to the Wheeler-DeWitt
equation which, as a semiclassical analysis shows, exhibit a good correlation
with the classical regime. We use the resulting wave functions to investigate
the possibility of removing the classical singularities.
