'morality of genuine pure conduct', 

consists in right speech, right bodily action and right livelihood, forming the 3rd, 4th and 5th links of the Eightfold Path (s. sacca, IV.3, 4, 5); cf. Vis.M. I. 

In A. II, 86 it is said:

"With regard to those moral states connected with and corresponding to the genuine pure conduct, he is morally strong, morally firm and trains himself in the moral rules taken upon himself. After overcoming the 3 fetters (ego-belief. sceptic doubt and attachment to mere rules and ritual; s. samyojana) he becomes one who will be 'reborn seven times at the utmost' (s. Sotāpanna) and after only seven times more wandering through this round of rebirths amongst men and heavenly beings, he will put an end to suffering."