Just so that there be no misunderstanding, let me clarify.
I myself have returned lost 20th-Century items I've found to their owner (or descendants).
At my age (mid-60s), I've also personally seen what happened to the lifelong relic-collections of quite a few digger friends and acquaintances who've passed away. They'd barely kicked the bucket before the descendants started turning the relics into money. Sometimes even the carefully written labels telling where a relic was found got discarded.
Unfortunately, it seems that darn few people nowadays care about what granddad or great-great granddad did "in the war."
So, what matters to me is getting the relics into the hands of somebody who deeply cares about their historical "meaning." Trust me that, generally speaking, a relic-digger (or collector) CARES about the relics a lot more than the average Museum staffperson. I've got personal experience in that area too. Museums (especially, governmen-owned ones) often trade or "de-accession" (meaning, sell) relics. Furthermore, museums tend to "lose" the relics (meaning, they get stolen by museum-employees). So, knowing what I know from personal experience, I've told my wife that if anything happens to me, I want her to sell all my relics to private collectors at an auction, or to one of my much-trusted longtime relic-dealer friends who will give her an honest value appraisal.
If you want your relics to be "treasured" (and very well taken care of) by their next owner, sell them to a relic-collector. Do NOT donate them to a government-owned museum. A major reason why Government-owned museum employees do not care deeply about the relics is that they didn't have to buy them with their own money.
All of the above being said... I agree with Crusader and Erik's suggestion. Contact whatever direct descendants you can find, and check whether they care about the historical information you can give them about their ancestor. If you do see genuine caring, send them photos of the ring (and the one showing Pvt. Richardson). As I've indicated in my statements above, it's all about caring, for "emotional" reasons, not just financial ones.