No, not really. "Morality in conduct of" does not follow the common understanding of the word, which is a nullable binary state which is either "moral" or "immoral" based on if the person adheres to the basic standard of civilized decency. (They could possibly be "ammoral", if they were ignorant of said basic standard due to being artificial or mentally impaired.)
A better expression is "morality of", which does not imply that morality is a flexable status. By example:
There is a deep gap between [the] morality of the officials and the public expectation.
Of course, if you want to imply that a speaker is less than truthful, you could use your construction to do so.
The official claimed he had "morality in the conduct of his official duties", but the numerous scandals over his personal affairs call that into question.