In canon, Jack Salem is not the Grim Reaper (yet), nor has there been any official suggestion that he would be.
The current reaper is Jack (not Jack Salem), and the one to follow him has been revealed recently (3 Arcs ago?). However, that person is not Jack Salem.
The Jack Salem as the sin Wrath (i.e., Grim Reaper) was set up for some rather humorous jokes comparing Jack (titled character) to Jack Salem as reaper. Whether Salem would ever become Reaper is unknown.
I have no idea how they divide work on collaborations. You could always just ask them.