LetRbe an associative ring not necessarily possessing an identity and (S, ≤) a strictly totally ordered monoid which is also artinian. Assume thatMis a leftR-module having property (F). We will show that there exists an isomorphism of rings.Therefore many properties of the endomorphism ring of leftR[[S, ≤]]-moduleMS, ≤]] may be induced from the properties of the endomorphism ring of leftR-moduleM.