  In the paper, we prove that there exists a braid group action on the extended
crystal $\widehat{B}(\infty)$ of finite type. The extended crystal
$\widehat{B}(\infty)$ and its braid group action are investigated from the
viewpoint of crystal similarity. We then interpret the braid group action on
$\widehat{B}(\infty)$ in the Hernandez-Leclerc category
$\mathscr{C}_\mathfrak{g}^0$.
