C-system of a module over a Jf-relative monad

Let $\mathbb{F}$ be the category with the set of objects $\mathbb{N}$ and morphisms given by the functions between the standard finite sets of the corresponding cardinalities. Let $Jf:\mathbb{F}\to Sets(U)$ be the obvious functor from this category to the category of sets in a given Grothendieck universe U. In this paper we construct, for any Jf-relative monad RR and any left RR-module LM, a C-system $C(\mathbf{RR},\mathbf{LM})$ and explicitly compute the action of the four B-system operations on its B-sets.In the introduction we explain in detail the relevance of this result to the construction of the term C-systems of type theories.