Let $A$ be an $\mathbb{E}_\infty$-ring spectrum, and let $R_1$, $R_2$ and $R_3$ be $\mathbb{E}_\infty$-$A$-algebras. We assume there is a homotopy fibre sequence $$ R_1\to R_2 \to R_3 $$ in the stable infinity category $\text{Mod}_{A}(\text{Sp})$. Then, is there a homotopy fibre sequence $$ K(R_1) \to K(R_2) \to K(R_3) $$ in $\text{Mod}_{K(A)}(\text{Sp})$?