  We consider moduli stacks of Bridgeland semistable objects that previously
had only set-theoretic identifications with Uhlenbeck compactification spaces.
On a K3 surface $X$, we give examples where such a moduli stack is isomorphic
to a moduli stack of slope semistable locally free sheaves on the Fourier-Mukai
partner $\hat{X}$. This yields a morphism from the stack of Bridgeland
semistable objects to a projective scheme, which induces an injection on closed
points. It also allows us to extend a theorem of Bruzzo-Maciocia on Hilbert
schemes to a statement on moduli of complexes.
