What should a person do with money they found, and its owner has not inquired about it after two years, despite a nearby shop warning people about it?

Informing the shopkeeper about the lost item is not enough. It must be publicized in the vicinity of its discovery and in places where its owner is likely to be found or to become aware of it. The obligation to publicize it does not cease with the passage of time. If you do not find its owner after a year of publicizing it, you may make use of it while guaranteeing it should its owner appear, based on the Prophet's (peace be upon him) saying: "Remember its tie and its container, then publicize it for a year. If it is not claimed, then spend it, and let it be a trust with you. If its owner comes seeking it one day, then give it to him."