reserve D,D9 for non empty set;
reserve R for Ring;
reserve G,H,S for non empty ModuleStr over R;
reserve UN for Universe;
reserve R for Ring;
reserve G, H for LeftMod of R;
reserve G1, G2, G3 for LeftMod of R;
reserve f for LModMorphismStr over R;

theorem
  for F being strict LModMorphism of R ex G,H being LeftMod of R, f
being Function of G,H st F is strict Morphism of G,H & F = LModMorphismStr(#G,H
    ,f#) & f is additive homogeneous
proof
  let F be strict LModMorphism of R;
  consider G,H such that
A1: F is Morphism of G,H by Th9;
  reconsider F9 = F as Morphism of G,H by A1;
  consider f being Function of G,H such that
A2: the LModMorphismStr of F9 = LModMorphismStr(#G,H,f#) &
f is additive homogeneous
  by Th7;
  take G,H,f;
  thus thesis by A2;
end;
