Though Mundungus is a member of the Order of the Phoenix, he's not especially brave or even all that committed to the cause—he's better known as a thief and a cheat, but he was brought into the Order because of his knowledge of other criminals. He is easily manipulated and is also extremely cowardly: Mundungus panics during the move and Disapparates, leading to Mad-Eye Moody's death.
Mundungus Fletcher Character Timeline in Harry Potter and the Deathly Hallows
The timeline below shows where the character Mundungus Fletcher appears in Harry Potter and the Deathly Hallows. The colored dots and icons indicate which themes are associated with that appearance.
...Harry as Mad-Eye Moody, Hermione, Fred, George, Bill, Mr. Weasley, Tonks, Lupin, Fleur, Kingsley, and Mundungus Fletcher file into the kitchen. Tonks gleefully waves her new wedding ring at Harry, but... (full context)
...Fleur fly into sight. Mrs. Weasley flies at Bill, who says that Moody is dead: Mundungus panicked and Disapparated, and Voldemort got Moody. Harry can't believe it. They head inside and... (full context)
...to explore the upstairs bedrooms. Someone went through them roughly. Harry wonders if it was Mundungus or Snape. He goes up another floor and enters Sirius's room. The walls are plastered... (full context)
...He forbids Kreacher from muttering insults and learns that Kreacher did steal the locket, but Mundungus Fletcher then stole "Master Regulus's locket." Harry stops Kreacher from punishing himself. (full context)
...passed information to them. Harry gives Kreacher a moment and then asks him to find Mundungus so they can find the locket. Kreacher nods, but dissolves into tears when Harry presents... (full context)
...shifts, and Dumbledore's portrait tells Snape to plant the idea for the seven Harrys with Mundungus. Snape digs through Grimmauld Place, pockets the last page of Lily's letter, and then Phineas... (full context)