Weak containment and conjugate subgroups of the Bohr compactification

Let $G$ be a finitely generated group. Let $G \curvearrowright^\pi \mathcal{H}$ be an orthogonal representation, and let $G \curvearrowright^{\pi'} \mathcal{H}'$ be an irreducible orthogonal representation. Write $b\mathcal{H}$ and $b\mathcal{H}'$ for the Bohr compactifications associated with these representations. Weak-containment conjecture. The representation $\pi$ weakly contains $\pi'$ if and only if there is a closed, $G$-invariant subgroup $K \subseteq b\mathcal{H}$ such that the topological algebraic actions $G \curvearrowright K$ and $G \curvearrowright b\mathcal{H}'$ are conjugate. This proposes that the Bohr compactification records precisely the weakly contained irreducible representations, extending the preceding result in one direction; the question is left open for future research.