Cowling's conjecture on weak amenability and the Haagerup property

Let $G$ be a locally compact group. The Haagerup property equivalence conjecture. $G$ has the Haagerup property if and only if $G$ is weakly amenable with $\boldsymbol\Lambda(G)=1$.

The conjecture was proposed as a link between weak amenability and the Haagerup property, both of which generalise amenability. It is refuted: groups such as $fmathbb{Z}\wr\mathbb{F}_2$ have the Haagerup property but are not weakly amenable, so the equivalence fails. The converse implication is stated separately as the remaining open version of Cowling's conjecture.