[The_Judge]

In theory, that is how it should work. The arrival city cleans the aircraft on the turn and they find all the lost items passengers left. In reality, a lost item many times is lucky to be found the same day, if at all. Smaller cities (and even the larger ones now with more staff) rarely have the luxury of time to go on board and pick up the big chunks on a turn. (Turn meaning an arrival and departure) Also, in theory, all aircraft are supposed to have a thorough cleaning when it sits overnight. This is when most items are found (that haven't been stolen by other passengers throughout the day).

So to be honest, the next arrival city may very well not find a left article on a plane and it honestly could ride the rest of the day or longer depending.