Seven paintings that were temporarily on display at the Kunsthal Museum in Rotterdam were stolen in 2012 in a raid that lasted only three minutes, in what the Dutch media called "the theft of the century".
A court in the Romanian capital ordered the heist's mastermind Radu Dogaru, his mother Olga, Eugen Darie and Adrian Procop to reimburse the paintings' insurers.
Prosecutors put the total value of the haul at over USD 24 million while art experts at the time of the heist had claimed the paintings were worth up to 100 million euros.
She later retracted the statement but a separate investigation is under way to determine if the masterpieces did end up in ashes.
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Ernest Oberlander-Tarnoveanu, director of Romania's National History Museum, said evidence of "painting primer, the remains of canvas and paint" were found in the stove, but experts must determine whether the ashes came from the missing paintings.
The works include Monet's "Waterloo Bridge, London" and Picasso's "Harlequin Head". None of them was equipped with an alarm.
"In the first place, we don't believe the stolen paintings were the originals and secondly it is up to the museum to pay because it took the stupid risk of displaying the artwork without a proper surveillance system," he added.
The paintings had been loaned to the museum for a show to celebrate its 20th anniversary by the Triton Foundation, which was set up to look after the art collection amassed by the Dutch investor Willem Cordia, who died in 2011.