  A morphism of the moduli functor of admissible semistable pairs to the
Gieseker -- Maruyama moduli functor (of semistable coherent torsion-free
sheaves) with the same Hilbert polynomial on the surface, is constructed. It is
shown that these functors are isomorphic, and the moduli scheme for semistable
admissible pairs $((\tilde S, \tilde L), \tilde E)$ is isomorphic to the
Gieseker -- Maruyama moduli scheme. The considerations involve all components
of moduli functors and corresponding moduli scheme as they exist.
