  A morphism of nonreduced Gieseker - Maruyama functor (of semistable coherent
torsion-free sheaves) on a surface to the nonreduced functor of admissible
semistable pairs with the same Hilbert polynomial, is constructed. This leads
to the morphism of moduli schemes with possibly nonreduced scheme structures.
As usually, we consider subfunctors corresponding to main components of moduli
schemes.
