What does it mean by perfect morality?
In AN 3.88 Buddha gives definitions of the three trainings. Basically, sila is training in discipline (often translated as virtue or morality), samadhi is training in controlling one's mind and mood, and prajna is training in understanding or insight.

In my understanding and as per AN 2.19, training in discipline is first and foremost training to optimize your actions by their result (instead of being simply reactive or impulsive). You do what's wholesome (leads to good results) and abandon what's unwholesome (leads to bad results). You repeatedly train yourself to think objectively in terms of action and its results, not in terms of your personal desires and aversions. For most people this is a radical change in attitude!

However, at this level you do only a minimum amount of self-reflection. Your sole focus is on external activity. But in order to optimize your activity you are forced to suppress some of your baddest impulses, habits and reactions. Which naturally leads to emergence of self-reflection, you becoming self-aware, and going to the next level - training to control your mental and emotional state.

So when Buddha says, "accomplished virtue" - I believe he means that as far as your intention to accomplish the good, you are perfect. Your behavior is fully determined by your good will. However, because of imperfections in your ability to control your mind and emotions, and imperfections in your wisdom/insight into how things work, you may still misstep occasionally.

Notice how Buddha insists in AN 3.85 that to be a Sotapanna you must also be moderately accomplished in concentration, and moderately accomplished in discernment. Not just virtue! This is because virtue, concentration and discernment interpenetrate. You can't have good behavior without some amount of mind-emotion-control and some amount of wisdom.

So in short, in my understanding the perfect morality is wholesome behavior and wholesome speech, based on wholesome intent, based on the right view - the first five and a half steps of the Eightfold Path.

Of course to say that one's behavior can ever be perfect is a (useful) simplification. As Buddha himself says in AN 3.85 you may still "fall into offenses and [later] rehabilitate yourself". But as far as your appreciation of the notion of kusala/akusala and your sincere attempts to act kusala, as far as your attitude - they are perfectly complete. You attitude has been completely reoriented towards the good result. That's what makes you a Sotapanna.