Let Z(R) be the center of a ring R and \(g(x)\) be a fixed polynomial in Z(R)[x]. In this paper, we continue the study of weakly \(g(x)\) -invo clean rings. A ring R is called weakly \(g(x)\) -invo clean if each element of R is a sum or difference of an involution and a root of $g(x)$. We determine the necessary and sufficient conditions for the skew Hurwitz series ring \((HR,\alpha )\) to be weakly \(g(x)\) -invo clean, where \(\alpha\) is an endomorphism of R. We also prove that the ring of the skew Hurwitz series \((HR,\alpha )\) is weakly invo-clean if and only if R is weakly invo-clean.
