Gordon Park hanged himself in his prison cell in 2010 while serving a life sentence for the murder of his first wife Carol, also a teacher.
Park, who always maintained his innocence, was convicted at Manchester Crown Court in 2005 and lost an appeal three years later.
His conviction has now been referred to the Court of Appeal by the Criminal Cases Review Commission (CCRC), which investigates potential miscarriages of justice.
Three senior judges will hear the appeal, which is based on new forensic evidence and concerns about disclosure, over three days starting on Tuesday.
Carol Park went missing from the family home in Leece, near Barrow-in-Furness, Cumbria, in July 1976.
Park claimed she had vanished from their home to live with another man, but the mother-of-three's body was found by divers in Coniston Water in the Lake District in 1997.
Following the discovery, he was arrested and charged with her murder, but the case against him was dropped in 1998 on the grounds there was not enough evidence available at the time.
Detectives later uncovered fresh forensic and geological evidence said to link him to the murder and he was found guilty in 2005, bringing to an end one of Britain's most notorious unsolved murder investigations.
Following his death at HMP Garth in Lancashire, his family continued to campaign for his conviction to be overturned and applied to the CCRC.
Lawyers for the commission will argue that the safety of the prosecution against Park is undermined by non-disclosure of evidence relating to the murder weapon, said to be an ice axe he used for climbing.
They will also present new scientific evidence which they say shows Park was not a contributor to DNA found on knots of rope used to bind Mrs Park's body, and argue that expert evidence which ruled out a link between a rock used to weigh the body and rocks at the family home has "renewed relevance".
The appeal hearing will start at 10.30am.