Commutativity preserving mappings in Banach algebras

Let $A$ and $B$ be unital complex Banach algebras having no quotients isomorphic to $\mathbb{C}$ or $M_2(\mathbb{C})$. Assume additionally that $B$ is semisimple. If a surjective additive mapping $\mathrm{\Phi }\text{\hspace{0.17em}⁣}:A\to B$ satisfies $[\mathrm{\Phi }(x^2),\mathrm{\Phi }(x)]=0$ for all $x\in A$, then there exist a surjective direct sum of an additive homomorphism and an additive anti-homomorphism $\mathrm{\Psi }\text{\hspace{0.17em}⁣}:A\to B$, an invertible element $\lambda \in \mathcal{Z}(B)$, and an additive mapping $\zeta \text{\hspace{0.17em}⁣}:A\to \mathcal{Z}(B)$ such that $\mathrm{\Phi }(x)=\lambda \mathrm{\Psi }(x)+\zeta (x)$ for all $x\in A$.