Artinian rings related to relative almost projectivity. II (Q1911580)

In part I [ibid. 32, No. 1, 135-153 (1995; Zbl 0827.16017)] the author studied an artinian ring \(R\) for which the following condition holds: for \(R\)-modules \(M\) and \(N\), if \(M\) is \(N\)-projective, then \(M'\) is always almost \(N\)-projective for every submodule \(M'\) of \(M\). The author gives a characterization of \(R\) for which the above condition is satisfied for any \(R\)-modules \(M\) and \(N\).