Clozel's algebraicity conjecture for inner forms of general linear groups

Let $G'$ be the inner form of a general linear group considered in the paper, let $G'(d538)$ denote its adelic points, and let $d4ab'$ be a discrete series automorphic representation of $G'(d538)$ such that its global Jacquet–Langlands transfer $JL(d4ab')$ is cuspidal. Write $d4ab'_f$ for its finite part.

Clozel's conjecture. The following are equivalent:

1. $d4ab'_f$ is defined over a number field.
2. $d4ab'$ is algebraic.

This generalizes Clozel's corresponding conjectures from split general linear groups to their inner forms, under the hypothesis that the Jacquet–Langlands transfer is cuspidal. The source presents this as a proposed generalization; no resolution is given.