Representation of H-closed monoreflections in archimedean `-groups with weak unit

The category of the title is called W. This has all free objects F(I) (I a set). For an object class A, HA consists of all homomorphic images of A-objects. This note continues the study of the H-closed monoreflections (R,r) (meaning HR=R), about which we show ({\em inter alia}): A∈A if and  only if A is a countably up-directed union from H{rF(ω)}. The meaning of this is then analyzed for two important cases: the maximum essential monoreflection r=c3, where c3F(ω)=C(\RRω), and C∈H{c(\RRω)} means C=C(T), for T a closed subspace of \RRω; the epicomplete, and maximum, monoreflection, r=β, where βF(ω)=B(\RRω), the Baire functions, and E∈H{B(\RRω)} means E is {\em an} epicompletion (not ``the'') of such a C(T).