Returning things like that is often the easiest thing to do. Also they probably have sentimental value to them that doesn't exist to you, if you keep them people might think you have stolen it, if it's very valuable and they're not that rich it would be a very bad thing for them and you can't let it happen, if they're very rich then they might afford to lose it but it probably has sentimental value and besides, if they were really rich they might reward you... once I found someone's mobile telephone and it was completely useless to me any way, so I brought it to a lost and found, I mean why keep it, I suppose some enterprising person can find a way to sell it to people who can use it but it would be lots of trouble and not worth it and then there's the fact that the easiest thing for everyone would be for people to return things and though you can't guarantee that your lost items will be returned better it is to not be part of the problem...
That homeless person could have said "that's a nice donation" and justified keeping it but if he did keep it what would he do with it. Unless he sells it it can't help him in any way, and selling it would bring lots of possible trouble. Some shady characters probably would have profited the most of it. It's better to tell those people that the ring was left with him so that if they really wanted to give it to him that this could be confirmed or in all likelihood, not.