RE: Start centerboard?
Yes, he could easily make a plug.
Just get a small piece of wood that's about 5/8" thick (the plug should finish up at about 0.620" thick, lay his fin on top of the board and draw the profile of the fin head.
Then a little work with a saw, the radius the ends, sand the board down until it fits easily in the fin box,
Be sure to get some wood that won't "swell" when wet as this could damage the fin box.
Drill a couple of pilot holes with the block fully inserted in the board, install a couple of 6mm inserts and he would have a very nice fin box plug.
Another option would be to get a broken off fin and grind off all the broken part until you have a nice flat surface that matches the bottom of the board (profile).
Even with no plug, not that much water will come up through the box.
Another option is to take a piece of good tape and simply tape over the center fin slot.
Hope this helps,