It's impossible to make the determination and to be 100% sure that he won't be susceptible to more concussions. The people most susceptible to getting concussions are those that have had one before (then 2, then 3 and so on), so I think technically, he will always be at a theoretical higher risk. The only thing a doctor can do is monitor symptoms if they are present and counsel him and his family appropriately.
If he's not exhibiting any symptoms, then there's no reason he can't play if he wants to, but it's up to the doctor to clearly explain the risks and potential of future concussions so that he and his family can make an informed decision. The problem is that concussions don't act the same for everyone; some people have a second concussion a year removed from the first and experience the effects of that for a long time (i.e. Ash), some people have their 2nd concussion in 6 months and get over it fine. Some people get a first concussion and symptoms last a few days, some people it lasts a month. And it has no correlation with how they were injured or the perceived intensity of the impact. Some people get punched or kicked in the head and don't get a repeat concussion, some people get symptoms if they try to head a soccer ball. So it is very difficult to say for certain or to predict a quantifiable risk. Naturally this changes if you've had 3, 4, 5 concussions etc... But at 1 or 2, you leave it up to the player and their family (as long as they're symptom free) and make sure that they know to report any symptoms as soon as they happen.