Cornelius Gurlitt’s notarized will, which did not surface until after his unexpected death this past May, lists the Kunstmuseum Bern in Switzerland as the heir to his vast art collection, which included works by Matisse, Dix, and Chagall. The unusual legal issue here: one month before his death, Conelius Gurlitt agreed to return all Nazi-looted artworks in his possession to the offspring of the rightful owners.

Gurlitt, who had been living in what some publications have called a “squalid apartment,” apparently hid some of his $1.35 billion art collection in a closet in his modest Munich flat. The current Bavarian government, which had been investigating Gurlitt for tax evasion as early as 2010, first discovered his trove after raiding his apartment in 2012. German authorities knew that some of Gurlitt’s works could be looted, but for unclear reasons, possibly stemming from fears of a deluge of legal claims from victims of Nazi art-looting, declined to alert the public of the discovery for almost two years.

A special government-appointed German task force is analyzing the provenance of about 600 works of art, of the roughly 1,400 in Gurlitt’s cache, to determine whether they had been looted or sold under duress during Nazi reign. Those pieces that the task force deems to be plundered by Hitler’s regime are expected be returned to the descendants of the victims of the art-looting Nazis. Descendants of Paul Rosenberg, a Parisian-Jewish art dealer before the Nazi invasion of France, will likely be restituted a $20 million Matisse painting after the task force determined Wednesday that the piece had been looted from a bank vault in southern France. According to the German investigators, the decision to return the painting now lies with Gurlitt’s heir.

The clock is ticking for the task force, as Bavaria’s justice ministry now has less than a year to comb through Gurlitt’s collection, per the terms of an agreement with the late recluse.

Legal complications may arise if Kunstmuseum, which has not yet accepted the inheritance despite proclaiming itself the “unrestricted and unfettered sole heir” to Gurlitt’s collection, attempts to take possession of the paintings before the conclusion of the government investigation.

Although there are nonbinding international codes of ethics at play here, such as the Washington Conference Principles on Nazi-Confiscated Art, there has been little indication in the media as to whether and how Kunstmuseum, once it is in possession of Gurlitt’s cache, would return any works subsequently found to be looted.

Also unclear is whether German authorities will be held liable by the victims’ families for keeping the discovery of Gurlitt’s collection under wraps for so long.

Background info: Beginning in the 1930’s and continuing throughout World War II, the Third Reich engaged in a “cultural cleansing” by looting thousands of works of art owned by prominent Jewish families throughout Europe. Many collectors, whose artwork escaped Nazi confiscation, were nonetheless blackmailed into conducting fire sales of their collections. The plundered pieces were often destroyed, sold to the highest bidder, or kept by various Nazi officials. Modern laws enable descendants of the Nazi art victims to reclaim what was plundered by Hitler’s regime.