How to recover apps from iPhone to iTunes?

I lost my Mac (logic board), and wasn't using Time Machine (long story). I had backed up all my music, photos, files, etc but not my apps.

I have a new iMac, and now iTunes doesn't recognize the iPhone. I allowed it to initialize the phone and re-synch the music, but if I re-synch the apps (there aren't any on the imac) it says its going to remove the apps from the phone?

Is there a way to manually move them back to iTunes so I don't lose them on a synch?