A former post office worker committed suicide after he was wrongly accused of stealing £60,000.
Martin Griffiths took his own life in 2013 at the age of 59.
According to The Times, Mr Griffiths delved into his own savings to make up for the deficit.
His sister, Jayne Caveen, said last year that a “bloody faulty computer system killed my brother”.
Mr Griffiths is one of many post office workers who died with convictions against their names and their lives were “irreparably ruined” after they were wrongly prosecuted by the Post Office.
Lawyers representing 42 former employees said evidence of serious defects in the Horizon system was “concealed from the courts, prosecutors and defence”, in order to protect the Post Office “at all costs”.
Their convictions were referred to the court by the Criminal Cases Review Commission (CCRC) last year following a landmark High Court case against the Post Office.
The Post Office conceded that 39 of the 42 former subpostmasters should have their convictions overturned on the basis that “they did not or could not have a fair trial”.
But it opposed 35 of those 39 cases on a second ground of appeal, which is that the prosecutions were “an affront to the public conscience”.
At the Royal Courts of Justice in London on Friday, 39 of the former subpostmasters finally had their names cleared.
Announcing the court’s ruling, Lord Justice Holroyde said the Post Office “knew there were serious issues about the reliability of Horizon” and had a “clear duty to investigate” the system’s defects.
But the Post Office “consistently asserted that Horizon was robust and reliable” and “effectively steamrolled over any subpostmaster who sought to challenge its accuracy”, the judge added.
Following the ruling, Mr Griffiths nephew Samuel Caveen, said: “Today’s news is welcome, but a reminder that not everyone in the Post Office scandal was prosecuted; some just had their livelihoods, reputations, life savings and wellbeing stolen from them. The fatal effects of that cannot be overturned by a judge.”
In a statement after the ruling, Post Office chairman Tim Parker said: “The Post Office is extremely sorry for the impact on the lives of these postmasters and their families that was caused by historical failures.
“Post Office stopped prosecutions soon after its separation from Royal Mail a decade ago and has throughout this appeals process supported the overturning of the vast majority of convictions.
“We are contacting other postmasters and Post Office workers with criminal convictions from past private Post Office prosecutions that may be affected, to assist them to appeal should they wish.”