Is it permissible to return a lost item to its place after many days have passed, with the possibility of it being taken by whoever finds it, due to the difficulty of identifying its owner (the need to spend money to copy identification papers, or going to public places to identify it with embarrassment)?

Whoever takes a found item (luqata) to safeguard it for its owner is obligated to do one of two things: either publicize it (ta'reef), or relinquish possession of it. Relinquishing possession means handing it over to the judge or his representative. If neither is available, then it means returning it to the place where it was found, though there is a difference of opinion among scholars regarding liability (daman) if he returns it to the place where it was found. The Malikis and Hanafis do not consider him liable, while the Shafi'is and Hanbalis consider him liable. The opinion of liability is more sound.