If someone found books that have an identifying mark, he must not read from them, but must keep them in an appropriate manner for the owner.
If he wishes to give them to someone else whom he trusts to look after them, he may do so. This is speaking about an object which was lost. If someone deposited an item in his charge, however, he may not give it to someone else to look after on his behalf.
If the person wishes to travel to another place and does not wish to take the item with him because it would be difficult or a big responsibility, then he can hand it over to a Beth Din (Jewish court), who, in turn, can give it over to someone else whom they consider reliable.
(See Ben Ish Hai, 1st year, Parashath Ki Thabo, Oth Zahn)