Lord Advocate, James Wolffe QC has applied to the High Court for authority under Double Jeopardy laws to set aside the acquittal of Sean Flynn.
Ms Tiffney, 43, was last seen leaving her flat in Dean Village, Edinburgh, after a row with Mr Flynn, then 18, in 2002.
In April last year Ms Tiffney’s remains were discovered near Gosford House in East Lothian.
Mr Flynn, then 21, stood trial at the High Court in Perth in 2005 accused of murdering his mother and disposing of her body but walked free on a not proven jury verdict after 22 days of proceedings.
A cyclist stumbled across Ms Tiffney’s remains on a secluded patch of scrubland on the Gosford House estate on April 2 last year – just yards from the A198.
The window dresser was last seen leaving her home in Dean Path, Edinburgh, on May 27, 2002.
Mr Flynn was charged with her murder in 2005 but walked free after a jury returned a not proven verdict.
A copy of Ms Tiffney’s death certificate states the cause as “unascertained pending investigation.”
Following the grim discovery last year, Dundee University’s world-renowned Centre for Anatomy and Human Identification were called in to help with the case.
They helped crack the grisly Philomena Dunleavy murder after the 66-year-old’s dismembered body was found in a shallow grave on Corstorphine Hill in 2013.
Detectives re-appealed for any witnesses to come forward a year on from finding Ms Tiffney’s body in April.
Ms Tiffney’s family are understood to have been kept updated on the inquiry’s progress.
Tory leader Ruth Davidson called for fresh impetus from officers on the anniversary of Ms Tiffney’s remains being found.
“This was a notorious Edinburgh murder which had a significant breakthrough last year,” said Ms Davidson, whose constituency covers Ms Tiffney’s former home.
“Her loved ones have suffered enough and deserve closure.”
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