Rubbina Shaheen was jailed for 12 months when she appeared before Shrewsbury Crown Court in December 2010.
She had been accused of stealing £43,000 from Greenfield Post Office which she ran in the town.
The theft charge was dropped on condition she admitted a lesser charge of false accounting.
But Mrs Shaheen has protested her innocence, saying it was a fault with the Post Office’s controversial Horizon computer system which caused the discrepancy.
The Criminal Cases Review Commission, which has the power to ask the Court of Appeal to reconsider cases, has appointed a team of forensic accountants to look into the claims.
Mrs Shaheen has been told that the experts will be looking into her claims about problems with Horizon, which logs all transactions at post office branches up and down the country.
The Post Office had previously appointed its own team of forensic accountants from Second Sight consultants.
Second Sight’s investigation found no “systemic problems” with Horizon, but said it was “not always fit for purpose” and that it was possible failings with the system could have caused discrepancies.
In a letter from the CCRC’s case review manager, Miles Trent, Mrs Shaheen has been told that the investigation might take a number of months, and that she would be updated on progress by the end of October.
Mrs Shaheen’s husband Mohamed welcomed the news.
“I think there are 30 cases which the Criminal Cases Review Committee is investigating, ” he said.
“It is taking time, but it is good news that a team of forensic accountants are investigating, and I am hoping we will know more by the end of the year.”
Mrs Shaheen is one of about 1,500 post office managers past and present who claim they have been wrongly blamed for financial discrepancies caused by the Horizon system.
In a separate action, lawyers representing 522 current and former sub-postmasters have handed in their evidence for a group legal action against the Post Office over claims.
Justice For the Subpostmasters Alliance, which is bringing the action, claims that postmasters wrongly blamed for financial shortfalls were made to sit in darkened rooms and told they were the only ones who had problems with the Horizon system.
Mr Shaheen said his wife had chosen not to take part in that action because she was concentrating on getting her conviction overturned.
The Post Office’s Mel Corfield said the organisation would be defending this case.
“We will be continuing to address the allegations through the court’s processes and will not otherwise comment on litigation whilst it is ongoing.”
She added that nearly 500,000 people had used Horizon since it was introduced, and at the moment there were about 78,000 users across 11,600 branches nationwide using the system to process six million transactions a day.