Transfer of R-groups between p-adic inner forms of $\operatorname{SL}_n$

Let $F$ be a non-archimedean local field, let $M$ be a Levi subgroup, and let $\phi: W_F\times \operatorname{SL}_2(\mathbb{C})\to \widehat{M}$ be an $L$-parameter. Let $\Pi_\phi(M)$ be its $L$-packet, and for a discrete series representation $\sigma\in\Pi_\phi(M)$ let $R_\sigma$ denote its Knapp–Stein $R$-group. Define the Arthur $R$-group by

$$R_{\phi,\sigma}:=W_{\phi,\sigma}/W_{\phi,\sigma}^{\circ}.$$

Transfer conjecture. For every discrete series representation $\sigma\in\Pi_\phi(M)$, one has

$$R_\sigma\simeq R_{\phi,\sigma}.$$

This asserts that the Knapp–Stein and Arthur $R$-groups agree for representations in the same $L$-packet. The supplied text does not state whether the claim has been proved or disproved.