Perfect-Prismatic F-Crystals and p-adic Shtukas in Families

We construct an equivalence between the two categories in the title, thus establishing a link between Frobenius-linear objects of formal (schematic) and analytic (adic) nature. We will do this for arbitrary p-complete rings, for objects equipped with an action by an arbitrary affine flat group scheme over Zp and without making use of the Frobenius-linear structure