Ms Grace said the officers' patience was wearing thin, so they searched the area where the teen had come running from.
There they found clothing and a bag containing a New Zealand Defence Service Medal, cash, a gold watch, cufflinks, rings and a locket.
The teen denied having anything to do with the items, but police arrested him and charged him with breach of bail.
Ms Grace said the teenager was expected to face further charges when he appeared in court this afternoon.
Police today identified the victim through his medal, which had bars for territorial and national service.
However, they were yet to speak to the victim directly.