  Let $K$ be a complete discretely valued field of mixed characteristic $(0,p)$
with perfect residue field, and let $E$ be a finite extension of $\mathbf{Q}_p$
contained in $K$. We show that the category of prismatic $F$-crystals on
$\mathcal{O}_K$ (relative to $E$ in a suitable sense) is equivalent to the
category of $\mathcal{O}_E$-lattices in $E$-crystalline representations defined
by Kisin--Ren, extending the main result of \cite{arxiv:2106.14735} in the case
$E=\mathbf{Q}_p$.
