There are numerous moral qualities which can be discussed but let us firstly focus on the first word from this syntagma – moral. If we look at Cambridge dictionary to help us define morality, here’s what we’ll find under the term ‘moral’: „relating to the standards of good or bad behaviour, fairness, honesty, etc. that each person believes in, rather than to laws.“ 
It is obvious that moral behaviour correlates to what we as human beings regard as „the right thing to do“ in agreement with our emotions and some generally shared moral principles of human behaviour. Therefore, moral qualities have nothing to do with law. For example, slavery was once legal (the law permitted its practice), but it is not morally „right“ nor acceptable.
According to Long and Sedley, the term ‘morality’ comes from the Latin word ‘moralis’, meaning manner, character, proper behaviour; They define morality as the: „differentiation of intentions, decisions and actions between those that are distinguished as proper and those that are improper.“  Some commonly shared moral qualities and norms are e.g. kindness, thoughtfulness, faithfulness, patience, calmness, etc. These are also the characteristics of each person of moral character.
In short, moral qualities are those for which the possessor is the suitable recipient of the responsive attitudes. We can define morality and moral qualities as those tendencies of character for which it is appropriate to hold an individual morally responsible. A trait for which the individual is deserving of a positive responsive attitude, such as gratitude or praise, is a virtue, and a vice is a trait for which the individual is deserving of a negative responsive attitude, such as blame or resentment. Moral qualities are relatively fixed, stable and reliable dispositions of activity and affect which should be rationally informed.
 Internet: https://dictionary.cambridge.org/dictionary/english/moral [Accessed 20-10-2018]
 A. A. Long; D. N. Sedley, The Hellenistic Philosophers. Cambridge University Press. Cambridge, 1987.