Aharoni–Lovász strong-perfectness conjecture for perfect graphs with finite independent sets

Let $G$ be a graph such that every induced finite subgraph is perfect; call such a graph perfect in the source's infinite-graph sense. Call $G$ strongly perfect if every induced subgraph has a partition into independent sets and a clique meeting every member of that partition.

Aharoni–Lovász conjecture. Every perfect graph in which all independent sets are finite is strongly perfect.

The source presents this as a more general conjecture of which the fish bone conjecture is a special case. It cites the result as known in the literature, but the supplied text does not state whether the conjecture itself has been solved.