For perspective, how large are most of those coralites? And is he big enough to see if he's ball/dome or flat in colony shape?
Until I get more info, I'm going to say there are some Favites that look similar....don't think Favia as it appear the coralites are sharing walls, but maybe I'm seeing it wrong. There are some Favia that otherwise look similar. Goniatrea share walls too, but rarely look that poofy...usually more skeletal. Platygyra (aka Maze Brain) is also possible, but they don't always have uniformly shaped coralites...often having several mouths in a long coralite "run". Those are the more common ones for sure.
Faviidae is a very, very large family and there are a couple other Genus aside from those already mentioned that could be candidates as well. From a photo and quick browse of Corals of the World (which means completely winging it) my best guess from many possibilites is a Favites.
-Matt