Is one absolved of responsibility by returning a banknote ($20) to the place where it was found after four months have passed since its owner was lost and contact with him was severed?

Informing the shop owner about the found item is not sufficient. Rather, it must be announced in places where people gather (mosques and markets) and through media outlets, if possible, for a full year. However, if the amount is trivial, not typically sought after by common people, then there is no harm in taking and utilizing it. Otherwise, it is not permissible to benefit from it until it has been announced for a full year. Some scholars have set the minimal amount that does not require announcement at a quarter of a dinar. So, if twenty dollars is less than a quarter of a dinar, it is permissible to possess it without announcement.