Finite generation of relative log canonical algebras of semi-dlt pairs

We prove that the relative log canonical algebra of a semi-dlt pair $(X,Δ_X)$ projective over a scheme $T$ is finitely generated, equivalently, that $(X,Δ_X)$ admits a relative stable model, provided that the normalization admits a log canonical model over $T$, that $(X,Δ_X)$ admits a stable model o