Syntomic cohomology, extracted from the Frobenius fixed points of prismatic cohomology, is a basic motivic invariant of schemes in mixed and positive characteristic. Recent work of Bhatt--Lurie and Drinfeld geometrizes this theory and defines coefficients for syntomic cohomology as quasi-coherent sheaves on certain stacks. In this talk, I will explain how to completely describe these stacks, and therefore their categories of sheaves, in terms of Fontaine--Laffaille--Faltings modules in the special case of Frobenius liftable schemes. This result is closely related to recent results of Ogus, Terentiuk--Vologodsky--Xu and an announced result of Madapusi--Mondal, although a precise relationship remains elusive. While our result is of a classical flavour, the techniques involved use some recent conceptual advances in derived geometry, due to several authors, which I will also explain if time permits.