Does the Automorphism Group Generate the Endomorphism Ring in Rep(S, R)?

Let R be a principal ideal domain and let (S, ≤ ) be a finite poset. We consider the question whether the automorphism group of a representation Rep(S, R) generates the endomorphism ring of . A complete solution is given if R = k is a field except in the case of GF(2). Moreover, some partial results and helpful techniques are obtained for the general case of R being a principal ideal domain, not a field