The typical 20 gauge Ithaca 37 from that era has seen lots of use. It is not a terribly expensive gun to replace. Does your son in laws gun reside, unfired, in it's original serial numbered shipping box?
I doubt it. But, if it does, tell him to leave it there and buy a Mossberg 500 to shoot. I'd bet his 20 has thinning blue, and a few scars on it's stock, or an aftermarket recoil pad fitted-20 gauge 37s have a tendance to "kill on both ends" when fed high brass ammunition, and I'd bet this one has seen plenty. They were bought back then to shoot. People did that.
If the gun looks a lot like the second description I put up, tell him I said its OK to use it with anything. He will enjoy it, and won't hurt the thing a bit, even with modern steel loads.
Best,
Ted