The robber can be found in chapter 6 - "Mansion".
He will be hiding in one of the upper-left rooms. You have to wait for him to leave and then search at the position where he was sitting. It will take a good amount of time until he leaves, but it is still enough to find the item and then rush to the exit. Clear all enemies before you wait would be my advise.
DON'T go in there before he left, otherwise he will attack you and don't leave the Phoenix Key behind.