  Roughly speaking, by using the semi-stable minimal model program, we prove
that the moduli part of an lc-trivial fibration coincides with that of a
klt-trivial fibration induced by adjunction after taking a suitable generically
finite cover. As an application, we obtain that the moduli part of an
lc-trivial fibration is b-nef and abundant by Ambro's result on klt-trivial
fibrations.
