"I will accept an apology from Conor Murphy, when he comes out on national television and apologises to us.
"And when he has that done, I want him to go to the gardaí and the PSNI and give them the names of the IRA men that he spoke to."
Breege Quinn was speaking on RTÉ radio almost 12 hours after Mary Lou McDonald faced intense questioning on the matter of her son's murder.
During the televised leaders' debate on Tuesday night, Ms McDonald had been confronted with proof that her party colleague Conor Murphy had branded victim Paul Quinn a smuggler and a criminal.
Ms McDonald swiftly promised an apology from her Northern finance minister.
Twelve hours later, Breege Quinn was still waiting for that apology.
But she had already been waiting for 13 years.
It was November 2007 when Sinn Féin MLA Mr Murphy claimed on the BBC that "Paul Quinn was involved in smuggling and criminality and I think everyone accepts that".
He also said he had spoken to IRA members and had been told the IRA was not involved.
In her radio interview, Ms Quinn insisted she had no interest in politics.
But with dignity and bravery, she spoke of the deep scars left by the loss of her son Paul at the age of just 21.
"My husband hasn't gone anywhere since Paul died.
"Any functions, any weddings, he doesn't go. The only place he goes, every day is to the grave, hail, rain or snow. And if it's lashing rain, he'll park outside the grave."
Her other children, James and Cathy, who were both older than Paul, are "very, very angry", said Ms Quinn.
James previously told the Irish Independent: "When I saw Paul lying dead in a hospital bed, his body battered so badly that it was hard to even recognise him, I felt pure hatred.
"My blood was boiling that the Provos had reduced him to that state. I wanted revenge on them. But, thankfully, wise heads - loyal friends who stood by my family after the murder - spoke to me and I calmed down."
Asked about this yesterday, Ms Quinn said: "I have said to them two wrongs will never make a right.
"I don't want those people to go out to a shed, and [be] murdered like they done Paul. I want to see them in court, and in jail."
Turning to the matter of Mr Murphy's comments about her son, she said: "Why has he left us 13 years fighting, crying, and people are accusing us now of coming out when there's an election to look for justice for Paul.
"I want to tell them that I have been fighting morning, noon and night the past 13 years for justice for my son.
"Why did Conor Murphy go to the IRA? Nobody asked him to go to the IRA.
"On the night that Paul was murdered, the very next day every political party, some member came to this door, but not one Sinn Féin member.
"That was even before we said the IRA murdered him."
Ms Quinn also said that Mary Lou McDonald had "come out now because there's an election". "But I don't care about elections, I'm not political, and neither is my husband nor any of my family," she added.
"I would like to see Conor Murphy resign from all positions in Sinn Féin.
"There is no compassion whatsoever, regardless of what position he has.
"He was an MLA when Paul was murdered. He's a finance minister now. I would like to see him step down.
"If he makes it on national television and goes to the PSNI and gardaí... then, yes, we will speak to him."
Presenter Sean O'Rourke put it to Ms Quinn that it was the 10 men who killed her son in a shed outside Castleblayney, and not Mr Murphy, who had destroyed her family.
She replied: "Yes, it is. Yes. But, it's also Conor Murphy, keeping up the hurt that he has caused us calling our son a criminal.
"He too is a parent."
Ms Quinn still "lives in hope" that some day Paul's killers will be brought to justice.
"You have to live in hope, like if you've no hope sure, you've nothing to live for.
"And at the end of the day, we meet these people at all times but they can't look at us, they won't look at us.
"Our conscience is clear. Theirs are not.
"If God called me and alone I'm happy to go, I never took nobody's life, or supported any of those organisations."
Mr Murphy issued an apology to the family yesterday.