  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 main components of moduli scheme
for semistable admissible pairs are isomorphic to main components of the
Gieseker -- Maruyama moduli scheme
