The family of Joseph Murphy has hit out at authorities for the delay.
Forensic tests have confirmed that the bullet was fired from a military-issue weapon.
Mr Murphy, 41, a father of 12, was injured in Ballymurphy, west Belfast, in August 1971 and died 13 days later in hospital.
Nine others were also killed during a series of shootings by paratroopers over three days.
The shootings occurred during Operation Demetrius, when paramilitary suspects were being detained and interned without trial.
The bullet was found in the body of Mr Murphy in October 2015.
Mr Murphy's family have said that they believe he was shot at a military barracks after being injured and that the bullet may still be lodged in his leg.
However, his daughter, Janet Donnelly, said that the delay in examining the bullet had hurt her family as they have been unable to rebury him.
"I received the report a couple of days ago," she said.
"They know rightly my daddy hasn't been reburied yet and won't be until all these tests are completed. And they're sitting on their hands doing nothing."
Mrs Donnelly's solicitor Mark O'Connor said: "This is significant because it confirms what we already suspected - that there was a bullet lodged in Mr Murphy's body which wasn't picked up by a post-mortem.
"This will help us to establish the type of weapon used and potentially the trajectory that it entered Mr Murphy's body."
Mr Murphy was shot in the thigh and taken to the Henry Taggart army barracks, where he said he was shot through the open wound a second time.
Earlier this year, Coroner Jim Kitson told a preliminary hearing an exhumation order had been granted because of the "exceptional circumstances" of the case.
A bullet found in the exhumed body of a man killed in shootings in Ballymurphy in 1971 was not sent for forensic examination for three months.