At my previous job the son of the owner worked on our department, well I say "worked"........
He generally came and went as he pleased, disappeared for hours at a time, took extended tea and lunch breaks and the majority of his work had to be corrected by one of us, or worse, our manager. Despite one of the senior staff, who knew the owner for over 20 years, discussing this with the owner and our manager also having a word, nothing was ever really done. When he and I were put on a 3 day week he continued to receive 5 days pay...
I'd say no harm in casually dropping into a conversation that the person hadn't completed a task and see how your boss reacts. Or ask the person if they had finished the task you asked them to do, in front of the boss, it could be they would be pretty peeved if the other person was not pulling their weight. The company has employed you as a manager and you might find them more supportive than you think once they are aware of what's going on.
I'd definitely suggest not covering their work if you can avoid it and find subtle ways to show you are unhappy with their work/attitude.
GOOD LUCK!