Stability conjecture for Wick algebra $C^*$-algebras

Let $T: \mathcal{H}^{\otimes 2} \rightarrow \mathcal{H}^{\otimes 2}$ be a self-adjoint braided operator with $\lVert T\rVert < 1$. The associated $C^*$-algebra is $\mathcal{W}(T)=C^*(W(T))$. Stability conjecture for Wick algebra $C^*$-algebras. One should have

$$\mathcal{W}(T)\simeq\mathcal{W}(0).$$

This problem was posed in the cited literature as a question about the stability of isomorphism classes of Wick algebra $C^*$-algebras. Its resolution is not supplied in the source.