  We show a direct equivalence between the category of analytic/completed
prismatic $F$-crystals on the absolute prismatic site of a small (unramified at
$p$) base ring and the category of relative Wach modules from the theory of
$(\varphi, \Gamma)$-modules. The result is obtained by showing that the data of
the Galois action on a Wach module is equivalent to the data of a prismatic
stratification on the underlying $\varphi$-module.
