You go to counter, get a passport transfer form and take the copies of old and new passport ... They might ask your embassy to confirm its damaged but not a big deal as you're old passport and visa is on the computer.
If you haven't been abusing the visa excempt system, i,e. you don't have lots of in and outs you can just fly in and out a couple times, they won't bother you (they'll warn you before you get any trouble usually). You can also do 2 land border runs per year, so you're good untill next year at least.
There is no reason to be streased he can enter on tourist and do his voluntary work, no one is arresting legit volunteers from legit charitys he can do it on any visa for time being untill his tourist visa runs out and needs to switch. Be real here, in 13 years I have no ever heard of a volunteer or legit charity being harassed by immigration the ones being abused by visa mills are easily distinguished everything else is jobsworth advice.