Should this Christmas present thief be arrested?

Each year, our trashman leaves a Christmas card on our trash cans. This year, I decided to do something different, as a Christmas present for him. On trash pickup day before Christmas, I left an unopened bottle of beer with a $5.00 bill taped to it and a card saying HO HO HO Merry Christmas. The bottle was placed on the trash can the day of my trash pickup. Well, the trashman never received his Christmas gift. A neighbor tells me he witnessed a man grab the bottle of beer and run. Question: should this suspect be arrested? Here is why I ask this question. According to law,anything placed on public property is fair game for anyone, especially trash in trash cans. Since this was not trash, but rather a gift, does this law apply in this situation?