On Friday, Liverpudlian David Hunter (41), who flew into Ireland to carry out the killing, was jailed by the non-jury Special Criminal Court on his conviction for the murder of the manager of the Sunset House pub in Dublin more than four years ago.
He had denied the Kinahan Carte-ordered killing of Barr (35) at the pub - but he was convicted on the strength of DNA recovered from a ski-mask found discarded in the getaway car.
In January 2018, Eamonn Cumberton (32) of Mountjoy Street, Dublin 7, was also convicted of murdering the Tyrone native.
Writing on his social media account on Friday night, Michael Barr's father Colin 'Colly' Barr said: "It's so hard when you look at one of the murderers of your son, and you know that he was one of the last people to see your son take his last breath of air, and watch his head explode causing his death."
Earlier the grieving father had also praised the conviction of Hunter writing: "Great result in the courts today."
"Another Kinahan foot soldier won't be at the funeral of his father when he passes."
During the probe into Hunter's role in the Sunset House killing, gardai discovered he had also flown to Dublin from the UK on the morning of February 8, 2016 - the day before Gerry 'The Monk' Hutch's brother Eddie was murdered.
And he flew back out of Dublin Airport the following day.
Eddie Hutch Sr (58) was shot dead at his home in Poplar Row, Ballybough, in Dublin's north inner city on the night of February 8, in revenge for the Regency Hotel bloodbath which had happened just three days earlier.
There were a number of gunmen involved in the murder and there have been arrests but no charges yet in that case.
Sources say they are now investigating whether Hunter could also have been involved in that killing.
On the evening Barr, a well-known IRA figure from Strabane, was brutally gunned down, Hunter entered the Sunset House in north inner city Dublin with Cumberton before both fired multiple shots at Barr who was working in the pub on the night.
The victim, who was well-known to gardaí, was hit seven times.
Barr had been blamed by the Kinahan cartel for sourcing the weapons used in the Regency Hotel attack in which key cartel player David Byrne (34) was shot dead.
Gardaí believe Cumberton became involved in the Barr murder after owing a significant cocaine debt to the cartel.
Sources have also confirmed in the wake of Hunter's conviction, that gardaí have also now identified the suspected getaway driver for Hunter and Cumberton on the night of the murder.
This thug, originally from Cabra and a close associate of slain gangbosses Marlo Hyland and Eamon Dunne, is believed to have fled to Thailand in the wake of the killing.
Gardai suspect he is currently hiding out in the Middle East.
"A third suspect has been identified and is expected to be arrested in the coming months," the source said.
Hunter will get the mandatory life sentence for the murder of Michael Barr on November 2.