# The morphism between the moduli stack of filtered sheaves and of coherent sheaves

I am thinking about the morphism from the moduli stack of filtered coherent sheaf on $$X$$ to the moduli stack of coherent sheaves defined by forgetting filtrations,i.e.$$Filtcoh(X)$$ $$\rightarrow$$ $$Coh(X)$$(I am following the notation of the paper “ Components of the stack of torsion-free sheaves of rank 2 on ruled surfaces” by C.Walter ) ,where $$X$$ is a projective surface over an algebraic closed field $$k$$.

Is this morphism of algebraic stacks smooth? (at least flat ?)