Sookdeo's conjecture on S-integral points in backward orbits

Let $K$ be a number field with algebraic closure $\overline{K}$, let $S$ be a finite set of places of $K$ containing all archimedean places, and let $\varphi:\mathbb{P}^1\to\mathbb{P}^1$ be a rational map defined over $K$. For $\beta\in\mathbb{P}^1(\overline{K})$, define the backward orbit by

$$\mathcal{O}_{\varphi}^-(\beta)=\bigcup_{n\geq 0}\{y\in\mathbb{P}^1(\overline{K}):\varphi^n(y)=\beta\}.$$

A point is $S$-integral relative to $\alpha$ if no conjugate of it meets any conjugate of $\alpha$ at primes outside $S$. Sookdeo's conjecture. If $\alpha\in\mathbb{P}^1(K)$ is not $\varphi$-preperiodic, then for any $\beta\in\mathbb{P}^1(K)$, $\mathcal{O}_{\varphi}^-(\beta)$ contains at most finitely many points in $\mathbb{P}^1(\overline{K})$ that are $S$-integral relative to $\alpha$. This conjecture concerns uniform finiteness of $S$-integral points in backward orbits; the supplied text gives no resolution status, while attributing the conjecture to Sookdeo.