As a generalization of the Banach Stone Theorem, A. J. Lazar proved that for any two simplexes $K_1$ and $K_2$, $A(K_1)$ and $A(K_2)$ are isometrically isomorphic if and only if $K_1$ and $K_2$ are affinely homeomorphic.

Now, for two simplexes $K_1$ and $K_2$, if we consider a linear isometry from $A(K_1)$ into $A(K_2)$(not necessarily onto) then does there exists an affine continuous surjection from $K_2$ to $K_1$? Is it possible to obtain such an affine continuous surjection from the above result by Lazar?