There are numerous excellent oil finish products that could be used to do that. Timberluxe or a homemade mixture of 50% water-based spar varnish and 50% Tung oil ( the old Phil Pilkington product) come to mind. I would caution him to wait some time until there is no doubt all the added moisture from the rain has dissipated from the wood before applying anything.
Next time, suggest that he use preventative measures rather than corrective ones. A couple good coats of paste wax over the whole gun, wood and metal, goes long way toward protection from rain.
