Let * be an e.a.b. star operation on an integrally closed domain D, and let $Kgamma$(D, *) be the Kronecker function ring of D. We show that if D is a P*MD, then the mapping $D_{alpha}{mapsto}K{gamma}(D_{alpha},;{upsilon})$ is a bijection from the set {$D_{alpha}$} of *-linked overrings of D into the set of overrings of $K{gamma}(D,;{upsilon})$. This is a generalization of [5, Proposition 32.19] that if D is a Pr$ddot{u}$fer domain, then the mapping $D_{alpha}{mapsto}K_{gamma}(D_{alpha},;b)$ is a one-to-one mapping from the set {$D_{alpha}$} of overrings of D onto the set of overrings of $K_{gamma}$(D, b).