Under supervision from you is a first good step to take.
At school this would also need supervision.
To me its great that he wants to do it, but if it was me I would have to supervise...making sure dosage is right for activitys he's doing etc. does he always make sure he takes hypostoppers with him? If he is capable of remembering to take them with him and does it off his own back.. This maybe a time to let jim start doing his own injections... Under supervision in your home may be a good starting point...