Look at the thread in rifle hunting under sick/injured deer and that will give you some points of view. If it is still alive it should be fine to eat. Was it laying down or up moving fairly decent? If it was laying down from the injury get the poor shooter to go back and finish the job and save your tag. Either way I would not let it suffer. It may get sick this winter and infect the rest of the herd. Kill it, grill it, and invite the poor shooter over for supper.
Just my .02 cents.