Ugh, as a lifelong runner, I can relate. Shin splints are the worst! He needs to rest, ice and strengthen the muscle starting ASAP. Because if he continues to try to to push through, the forces being put on those underdeveloped muscles will be increasingly absorbed by the surrounding structures, including his bones, creating a stress fracture.
The one strengthening exercise I know of that works: get a 10 or 12 lb weight (ideally a circular weight, but any kind will do) and tie a rope or heavy cord to it. Make a loop in the cord so the weight can be dangled via the rope.
It will look something like this: 0-----[] 0 loop ---- cord [] weight
Leave about 6-8 inches of cord between base of the loop and the weight.
Then have him sit in a chair and put his foot through the loop. Stick his leg out straight and move the cord up to the flexion point at the base of his toes, so the weight is dangling from the top of his foot. Then have him move the weight up and down by flexing his ankle and toes. He shouldn't feel any pain, but done right, this exercise will precisely target and strengthen those problematic muscles.
Do a few sets a couple times a day. Adjust the weight and length of the cord as necessary. If he does this, and rests, he should start to feel better within 10-14 days.