Stamp #080 can be obtained by retrieving the Fluffy Mushroom from Mushroom Road forShirley. The Fluffy Mushroom is behind the Mushroom Road lake, during the nights it is strongly bright colored and can attract your attention so you can get it. When you get this to Shirley, you earn yourself a stamp.
You need to deliver the Uzumasa's autograph to Shirley before attempting to get this stamp.