Injectivity conjecture for skew Schur partition functions of two-row partitions

Let $\lambda'$ be a two-row partition, and let $\mathrm{prs}_{\lambda'}$ be the associated skew Schur partition function, defined on those partitions for which the function is defined. Two-row skew Schur injectivity conjecture. For every two-row partition $\lambda'$, the function $\mathrm{prs}_{\lambda'}$ is injective on $\mathcal{P}(n)$ for every positive integer $n$ on which $\mathrm{prs}_{\lambda'}$ is defined. This refines an earlier question about injectivity of these functions; no resolution is given in the supplied text.