The generalized strong isomorphism conjecture for Leavitt path algebras

Let $K$ be a field with a fixed involution, and let $E$ and $F$ be directed graphs. Write $L_K(E)$ and $L_K(F)$ for their Leavitt path algebras, equipped with the induced involutions. Generalized Strong Isomorphism Conjecture. If

$$L_K(E)\cong L_K(F)$$

as rings, then

$$L_K(E)\cong L_K(F)$$

as $^\ast$-algebras. The source introduces this as the stronger version of the Generalized Isomorphism Conjecture, but gives no resolution evidence in the supplied text.