  Finding the general set of system-environment states for which the reduced
dynamics of the system is completely positive (CP) is the subject of some
recent works. An advance in this context appeared in [X. Lu, Phys. Rev. A 93,
042332 (2016)], where the problem has been solved for the case of CP assignment
map. Here, we restate this result using the framework introduced in [J. M.
Dominy et al., Quantum Inf. Process. 15, 465 (2016)]. This, we think, clarifies
the mentioned result better and so leads to a generalization of it,
straightforwardly.
