Equality of perfectoid test ideals and multiplier ideals after inverting p

Let $(A,\fra^t)$ be a pair, where $A$ is the regular ring and $\fra$ is the ideal appearing in the construction of the perfectoid test ideal ${\mathrlap{\mJ}\,\,\uptau}(A,\fra^t)$. Let $A[1/p]$ be the localization obtained by inverting $p$, and let $\mJ(A[1/p],(\fra\cdot A[1/p])^t)$ denote the multiplier ideal of the corresponding pair over the characteristic-zero ring $A[1/p]$. Equality conjecture. One expects

$${\mathrlap{\mJ}\,\,\uptau}(A,\fra^{t})\cdot A[1/p]=\mJ(A[1/p],(\fra\cdot A[1/p])^t).$$

The paper proves the containment from left to right; the conjectured reverse containment would identify the perfectoid test ideal with the multiplier ideal after passing to $A[1/p]$.