Crewman Fuller was a member of the crew of Enterprise NX-01 during its mission in the Delphic Expanse. He was considered by Lieutenant Malcolm Reed to be the most knowledgeable in regards to the ship's torpedo systems.
Fuller became Enterprise's first fatality, when he was killed during a raid by Osaarian pirates in 2153. In engineering, he was shot at point-blank range by one of the Osaarians' particle weapons and fell from one of the engine's struts onto the deck below. (ENT: "Anomaly (ENT)")
In ultimately omitted dialogue from the final draft script of "Anomaly", it was established (in information Reed told Commander Tucker) that Fuller had gone through tactical training with Reed, that Fuller had a daughter who Reed had met a few years prior to 2153, and that Fuller had been "hand-picked" by Reed to serve on Enterprise. The script also established that Fuller's daughter had been in either second or third grade when she and Reed met, and that she had written a letter to Reed, after the ship left spacedock, in which she had asked him to keep her father away from dangerous missions.
There was also a female Crewman Fuller aboard Enterprise. In "The Expanse", T'Pol mentioned that "Crewman Fuller" informed her that a shuttle was arriving at Enterprise with two hundred snow beetles. However, since T'Pol did not use a specific pronoun to refer to this Fuller, it is unknown to which crewman she was referring.