The authors investigate the Hyers-Ulam stability for the following functional equation \[ \sum_{\varphi \in \Phi} \int_K f(xk\varphi(y)k^{-1})\;dw_K(k)=|\Phi|f(x)g(y), \quad x,y \in G, \leqno (E) \] where \(G\) is a locally compact group, \(K\) is a compact subgroup of \(G\), \(w_K\) is the normalized Haar measure of \(K\), \(\Phi\) is a finite group of \(K\)-invariant morphisms of \(G\) and \(f, g:G \to \mathbb C\) are continuous complex-valued functions. The main result of the paper is given by the following Theorem. Let \(\delta>0\) be given. Assume that continuous functions \(f, g:G \to \mathbb C\) satisfy the inequality \[ \Big| \sum_{\varphi \in \Phi} \int_K f(xk\varphi(y)k^{-1})\;dw_K(k)-|\Phi|f(x)g(y)\Big|\leq \delta, \quad x,y \in G, \] then {\parindent=6mm \begin{itemize} \item[i)] \(f, g\) are bounded or \item [ii)] \(f\) is unbounded and \(g\) satisfies the following so-called d'Alembert long equation \[ \sum_{\varphi \in \Phi} \int_K g(xk\varphi(y)k^{-1})\;dw_K(k)+\sum_{\varphi \in \Phi} \int_K g(\varphi(y)kxk^{-1})\;dw_K(k)=2|\Phi|g(x)g(y) \] or \item [iii)] \(g\) is unbounded and the pair \((f,g)\) satisfies the equation (E). If \(f \neq 0\), then \(g\) satisfies the d'Alembert long equation. \end{itemize}} This theorem generalizes previous results which required that the function \(f\) satisfies the following Kannappan type condition: \[ \int_K \int_K f(xkyk^{-1}hzh^{-1})\;dw_K(k)dw_K(h)=\int_K \int_K f(xkzk^{-1}hyh^{-1})\;dw_K(k)dw_K(h). \]