Automatic continuity and spatial form of biseparating maps between C*-algebras

Let $\mathcal{A}_{1}$ and $\mathcal{A}_{2}$ be $C^{\ast}$-algebras, and let $T:\mathcal{A}_{1}\to\mathcal{A}_{2}$ be a biseparating map, meaning that both $T$ and $T^{-1}$ preserve disjointness in the relevant algebraic sense. Let $\Psi:\mathcal{A}_{1}\to\mathcal{A}_{2}$ denote the associated map, and let $A_{0}$ belong to the commutant of $\mathcal{A}_{2}$. Automatic continuity and spatial-form conjecture. The map $T$ is continuous and

$$T(a)=A_{0}\circ\Psi(a),\qquad a\in\mathcal{A}_{1}.$$

The claim describes the expected structure of biseparating maps between $C^{\ast}$-algebras, combining automatic continuity with multiplication by an element commuting with the target algebra. The supplied text does not establish the assertion or state its resolution, so its status is left open.