I have to often take his work load or completely re-do more than

For most of these parts, I think my manager know they were my credit...

I just never know what's my manger's plan for how long to put us on the same projects.  Not indicate anything completely clear, my manager once mentioned very friendly or personally that he hope me to compromise the situation...there might be some politics beyong my awareness or beyond what my manger could do.

But again, when it goes beyong my limit, I will do: #1. confront his incapability, saying he should have done this and done that and if he does not do so, I can take over the rest part of the work untill he makes progress on his end.  if he gets frustrated in hearing me saying so, feel free to talk with the manager and I will talk all I have been worked for him.  #2. Talk with manager to ask for different assignment.