ANYwho....back to your question. It sounds like you have more than just this guy for a problem. The management that hired him has some trouble, too. And only you know what to do with him and the future. You have to evaluate what your goals are and how to meet them and act accordingly. There were a lot of times that I just did someone else's job cuz I NEEDED it to get done. The right people already knew that the person not doing his job was worthless in his role. So I had nothing to lose by doing his work, other than some time, and EVERYTHING to lose if his work didn't get done.
Sometimes we don't have the authority we think we need to accomplish our job. That problem is a problem for the manager as well as the employee. But you can only affect you. So you have to work within those parameters. And make your choice based on what's the most efficient, or what you are WILLING to do.
And when it REALLY sucks, and you are fed up, then you have to decide where you WANT to work. If it's not where you are, then you have to find what you DO want, and go there. You're only stuck for as long as you believe you are.