In The ShowEdit
Morfin first appears in episode 1 where he briefly greets Sir John Franklin while he's walking around the deck of Erebus. Later that evening, he is seen briefly alongside David Bryant as David Young is screaming from the nearby sick bay. He appears next in episode 2 when he is sent out with Lt. Gore's sledge party. Upon locating a message cairn on King William Island, Morfin cheers with enthusiasm. When he and some of the others return to camp, they find it wrecked to which Charles Frederick Des Voeux a bear must be nearby but Morfin questions if a bear was able to cause that much damage.
In episode 3, he and John Weekes are preparing the Netsilik Shaman's body for burial where they discover a large amounts of charms. Accompanied by Doctor Henry Goodsir and Des Voeux, Morfin and Weekes dump the body into a firehole. After Sir John is killed in the same episode he begins singing "The Silver Swan" in remembrance of him but is unable to remember the lyrics. Charles Best fills in the rest and he along with George Chambers, John Weekes, Morfin, and the rest of the men sing together.
In episode 4, Goodsir examines him and discovers he has gray gums due to lead poisoning and by episode 7, Morfin's health had declined considerably. One day he and Sgt. Solomon Tozer are out and patrol discover the remnants of Lieutenant James Walter Fairholme's sledge party. Later that evening the pain gets to a point where he can no longer stand it and after unsuccessfully begging/threating Crozier to put him down, he is shot by Tozer after firing a musket he obtained almost hitting Captain James Fitzjames.
In The BookEdit
Morfin joins Hickey's mutiny in the original book, although he doesn't partake in the cannibalism that the rest of the group does.