Summary: Let \(G\) be a simple graph, and \(G^\sigma\) be an oriented graph of \(G\) with the orientation \(\sigma\) and skew-adjacency matrix \(S(G^\sigma)\). The \(k\)-th skew spectral moment of \(G^\sigma\), denoted by \(T_k(G^\sigma)\), is defined as \(\sum_{i=1}^n (\lambda_i)^k\), where \(\lambda_1\), \(\lambda_2, \dots, \lambda_n\) are the eigenvalues of \(G^\sigma\). Suppose \(G^{\sigma_1}_1\) and \(G^{\sigma_2}_2\) are two digraphs. If there exists an integer \(k\), \(1 \leq k \leq n-1\), such that for each \(i\), \(0 \leq i \leq k-1\), \(T_i(G^{\sigma_1}_1) = T_i(G^{\sigma_2}_2)\) and \(T_k(G^{\sigma_1}_1)