In the remark on the bottom of page 5 of this paper, the author states that
It is well-known fact that the algebra of a Divisor $D$ with $\kappa (X,D) \leq 1$ is finitely generated over $k$. In fact, by the Iitaka fibration, there exists a variety $Y$ of dimension $\kappa(X, D)$, and divisor $D'$ on $Y$ such that $R(X,D) \cong R(Y,D')$.
Assume $X$ to be a complete normal algebraic variety.
Can anyone give a reference for this well-known fact, or elucidate the "$\cong$" in his brief explanation? Of particular interest to me is the case with $X$ a surface and $\kappa(D)=1$.