  We compute the twist-three fragmentation contribution to the transverse
single spin asymmetry (SSA) in light hadron production $p^\uparrow p\to hX$ and
$p^\uparrow A\to hX$ including the gluon saturation effect in the unpolarized
nucleon/nucleus. Together with the results in our previous paper, this
completes the full evaluation of the SSA in this process in the "hybrid"
formalism. We argue that the dependence of SSAs on the atomic mass number in
the forward region can elucidate the relative importance of the soft gluon pole
contribution from the twist-three quark-gluon-quark correlation in the
polarized nucleon and the twist-three fragmentation contribution from the final
state hadron.
