$H$-closed space

A Hausdorff topological space $ (X,\mathcal T)$ is called H-closed or absolutely closed if it is closed in any Hausdorff space, which contains $ X$ as a subspace.$ \newcommand{\ol}[1]{\overline{#1}}\newcommand{\mc}[1]{\mathcal{#1}}$ .

let$ (X,\tau_1) $ be a $ H$ -closed space and $ \tau_1 \subset \tau_2$ . Is $ ( X, \tau_2)$ a $ H$ -closed space?