Parabolic-induction compatibility for semisimple local Langlands

Let $bbM$ be a Levi subgroup of $bbG$, let $bbP=bbM\ltimesbbN$ be a parabolic subgroup, let $bbrho\inbbPi_{bbC}(bbM)$, and let $bbpi$ be an irreducible subquotient of $i_{bbP}^{bbG}(bbrho)$. Parabolic-induction compatibility conjecture. The semisimple parameters $bbiota_{bbM,bbG}\circ(bbmathcal{LL}_{bbM}(bbrho))_{ss}$ and $(bbmathcal{LL}_{bbG}(bbpi))_{ss}$ are $bbhat{bbG}(bbC)$-conjugate.

This is presented as the expected compatibility of local Langlands with parabolic induction; the source attributes it to Haines's Conjecture 5.22. The supplied text gives no resolution status.