Let R be a commutative Noetherian ring and \documentclass[12pt]{minimal}
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\begin{document}$\mathfrak{a}$\end{document} an ideal of R. We introduce the concept of \documentclass[12pt]{minimal}
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\begin{document}$\mathfrak{a}$\end{document}-weakly Laskerian R-modules, and we show that if M is an \documentclass[12pt]{minimal}
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\begin{document}$\mathfrak{a}$\end{document}-weakly Laskerian R-module and s is a non-negative integer such that ExtRj\documentclass[12pt]{minimal}
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\begin{document}$(R/\mathfrak{a},H_\mathfrak{a}^i (M))$\end{document} is \documentclass[12pt]{minimal}
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\begin{document}$\mathfrak{a}$\end{document}-weakly Laskerian for all i < s and all j, then for any \documentclass[12pt]{minimal}
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\begin{document}$\mathfrak{a}$\end{document}-weakly Laskerian submodule X of \documentclass[12pt]{minimal}
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\begin{document}$H_\mathfrak{a}^s (M)$\end{document}, the R-module \documentclass[12pt]{minimal}
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\begin{document}$Hom_R (R/\mathfrak{a},H_\mathfrak{a}^s (M)/X)$\end{document} is \documentclass[12pt]{minimal}
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\begin{document}$\mathfrak{a}$\end{document}-weakly Laskerian. In particular, the set of associated primes of \documentclass[12pt]{minimal}
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\begin{document}$H_\mathfrak{a}^s (M)/X$\end{document} is finite. As a consequence, it follows that if M is a finitely generated R-module and N is an \documentclass[12pt]{minimal}
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\begin{document}$\mathfrak{a}$\end{document}-weakly Laskerian R-module such that \documentclass[12pt]{minimal}
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\begin{document}$H_\mathfrak{a}^i (N)$\end{document}(N) is \documentclass[12pt]{minimal}
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\begin{document}$\mathfrak{a}$\end{document}-weakly Laskerian for all i < s, then the set of associated primes of \documentclass[12pt]{minimal}
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\begin{document}$H_\mathfrak{a}^s (M,N)$\end{document}(M,N) is finite. This generalizes the main result of S. Sohrabi Laleh, M.Y. Sadeghi, and M.Hanifi Mostaghim (2012).
