  The B_N hyperbolic Sutherland spin model is expressed in terms of a suitable
set of commuting Dunkl operators. This fact is exploited to derive a complete
family of commuting integrals of motion of the model, thus establishing its
integrability. The Dunkl operators are shown to possess a common flag of
invariant finite-dimensional linear spaces of smooth scalar functions. This
implies that the Hamiltonian of the model preserves a corresponding flag of
smooth spin functions. The discrete spectrum of the restriction of the
Hamiltonian to this spin flag is explicitly computed by triangularization. The
integrability of the hyperbolic Sutherland spin chain of B_N type associated
with the dynamical model is proved using Polychronakos's "freezing trick".
