Basically, I have an image that is to replace the green screen in the middle. But I have no idea how to get the image to mimic the motion of the wall. I tried motion tracking the wall but the track is too jumpy. Then I tried doing it by hand but, again, certain parts are jumpy. I asked the client if there was an AE file that went with the video and they are looking now. Didn't know what else to do so I turn to the Cow.
Dave and Roland have already suggested mocha which is probably your best bet, but I'll also take this opportunity to rant about stock videos with green screens. Many of them are poorly put together and show a lack of planning. In general I avoid them but when a client would like to use one I'd recommend encouraging them to check with you before committing to it. You're in the best position to tell them what will or will not work.
Now, back to this particular video. If learning mocha requires too much time in this case then I'd manually corner pin the footage over the green, key the green then place the corner pinned footage behind the keyed layer. The corner pin doesn't have to be perfect because the green key will define the edges of the video to be perspective correct and the edges are where any drifting or floating of the track would be most apparent.