Also worth consideration is whether diving on the injured ankle will cause any "secondary" injuries, set back any healing/progress your buddy has made already or cause any permanent injury.
I sprained my ankle last fall (2nd degree, close to 3rd degree) and was able to dive about 5 weeks later, but couldn't have managed more than one dive at a time. It was slow to heal in general, and at about 80% of "regular" functioning when I went on a liveaboard trip 4 months after the injury. After diving 4 dives/day for a week, I developed bursitis in the ankle joint from using the ankle so much with the ligaments still weakened. So after 6-8 weeks of letting that heal, and the extra use on my trip, I'm back to where I was in my general healing about a month before my trip. Whether he can actually dive on the trip may not be the only important thing to consider.