The Goodwin bothers were found guilty on Wednesday of killing the father-of-eight in August 2018.
The 33-year-old had been talking to a friend in Lee Bank, Birmingham, when a BMW and Mercedes pulled up and two shots were fired. One hit Mr Sargeant in the back and he died six days later in hospital.
The gun used in the shooting was recovered during a police raid in Derbyshire in November, 2019.
Experts from the National Ballistics Intelligence Service (NABIS) were able to prove it was the same weapon used to kill Mr Sargeant using unique markings on the weapon.
Ian Head, NABIS Head of Intelligence, Governance and International Development, said: “Firearms very often move around the UK from place to place and from crime group to crime group and once recovered NABIS are able to ballistically link them to previous firearms discharges.
"Evidence recovered from scenes allows NABIS to forensically link firearms that have been used in previous shootings. Upon receiving the evidence into our facilities NABIS forensic experts are able to connect scenes using state of the art technology.
"Firearms have unique markings in a similar manner to fingerprints that enable this forensic examination to take place. NABIS analysts then disseminate this ballistic intelligence to Senior Investigating Officers to assist with convictions as in this case."
Connor, 27, and Michael, 26, of Wallace Road, Oldbury, were found guilty of murder alongside Keenan Anderson, 25, of Albert Road, Handsworth, and 22-year-old Leon Riley, 22, of Bridgelands Way, Perry Barr.
As part of the investigation, detectives from West Midlands Police uncovered images showing the four celebrating Connor Goodwin’s birthday on the afternoon of August 26 at a pub in Hockley, less than 24 hours after the shooting and while Mr Sargeant lay dying in hospital.