usually boys stop growing around 17... but the key word there is usually, also growth plates don't all fuse at the same time... on the 17th birthday, usually the growth plates of smaller bones fuse first, then the long bones (which would add to height)... and when all this happens is determined by testosterone levels i believe.... it's 3AM, i'm not looking it up... theoretically, the easiest way to tell would be to look at an x-ray of his leg... if his growth plates have not fused you should be able to shoot him up with some growth and watch him grow... otherwise, get him a pair of nike shox... they make me look about 2 inches taller than i really am...
Best of Luck!