Between dierent and relatively well investigated so-called flatness properties of S-posets there is a property called property (Pw) which, so far, has not received much attention. In a recent paper by the author pomonoids from a subclass of completely simple semigroups with adjoined identity, all of whose cyclic (Rees factor) S-posets satisfy property (Pw), were characterized. In this paper pomonoids which as monoids are atomic semilattices, all of whose Rees factor S-posets satisfy property (Pw), are characterized.
