A military court in Jordan on Monday gave one of its soldiers a life sentence for shooting and killing three American special forces at a base near the capital Amman in November.
The soldier, Marik al-Tuwayha, had opened fire on the trainers in November as their vehicle approached al-Jafr airbase in November.
This is not the first time a USA service member was killed in the country.
Moriarty's father, Jim, wrote in a letter Monday to the Jordanian Embassy in the USA that the "successful prosecution" was a "good first step, but it is only the first step".
However, relatives of the slain US troops have described security camera footage that they say shows him shooting for six minutes, reloading and aiming at the Americans, even as they identify themselves as friendly forces.
Jordan, which hosts some 2,200 American military personnel, is a key American ally and a member of the US-led coalition fighting the Islamic State group in neighbouring Syria and Iraq.
It demoted him, removed him from military service and handed him a sentence of "hard labor for life".
Jordanian authorities at first said the USA trainers were shot because they failed to stop their vehicle as they drove up to the gate of a large air base. He is part of a tribe, the Howeitat, which on Monday issued a statement criticizing the court's judgment. About 2,000 USA troops are in Jordan.More news: Pelicans meet with PG Rondo
Surveillance video of the encounter was not publicly screened, but was shown to relatives of the victims.
Sergeant Tawayha said at his trial that he did not resent the American presence at the base.
A military court charged the soldier with murder and disobeying military orders.
In the letter, a copy of which was given to the AP, Moriarty listed several demands to Jordan.
Cynthia Lewellen, 53, the mother of Matthew Lewellen, expressed sympathy for all those affected by the shooting, including the family of the defendant.
In Jordan, life in prison can mean 20 years, with time off for good behavior.
US Embassy representatives who were present during the trial and judicial proceedings said they appreciated "the expedience and seriousness of the court proceedings" following the guilty verdict on Monday.
Jordan initially tried to shift the blame to the United States, saying the Americans triggered the shooting by disobeying entry rules, a claim that was later withdrawn.