Log canonical base conjecture for lc-trivial fibrations

Let $(X,\Delta)$ be a projective log canonical pair, and let $f:X\to Y$ be a contraction morphism between normal projective varieties such that

$$K_X+\Delta\sim_{\mathbb R,f}0.$$

Log canonical base conjecture. There is an effective $\mathbb R$-divisor $\Delta_Y$ on $Y$ such that $(Y,\Delta_Y)$ is log canonical and

$$K_X+\Delta\sim_{\mathbb R}f^*(K_Y+\Delta_Y).$$

The source states that this conjecture is open, including when $X$ is projective, and notes that it follows from the b-semi-ampleness conjecture for moduli parts of lc-trivial fibrations.