$K_X+B \equiv 0$ implies $K_X + B \sim_\mathbb{Q} 0$?

Let $$(X,B)$$ be a projective log canonical pair (here I mean $$B \geq 0$$). Assume that the coefficients of $$B$$ are rational, and that $$K_X+B \equiv 0$$. Is it true that $$K_X + B \sim_\mathbb{Q} 0$$? I know it is true if $$(X,B)$$ is klt, and "The moduli b-divisor of an lc-trivial fibration" by Ambro has a proof of it. I am curious whether the result extends to singularities that are lc and not klt, and, if so, where I could find a reference.

For lc pair or slc pair, it is true. This is Gongyo’s result. See [J. ALGEBRAIC GEOMETRY 22 (2013) 549–564].

BTW, the relative version is also true, which is not a trivial generalization of the absolute case. It is proved by Hacon and Xu [On Finiteness of B-representation and Semi-log Canonical Abundance].