The complex Leavitt path algebra ring-isomorphism conjecture

Let $E$ and $F$ be directed graphs, and let $L_{\mathbb{C}}(E)$ and $L_{\mathbb{C}}(F)$ be their Leavitt path algebras over the complex numbers, while $C^*(E)$ and $C^*(F)$ are the associated graph $C^*$-algebras. Complex ring-isomorphism conjecture. If

$$L_{\mathbb{C}}(E)\cong L_{\mathbb{C}}(F)$$

as rings, then

$$C^*(E)\cong C^*(F)$$

as $^\ast$-algebras. This is stated as an isomorphism conjecture in the source, and no resolution is given in the supplied text.