BERLIN—In the final days of World War II, Dresden art dealer Hildebrand Gurlitt packed his family, a supply of firewood and the works of some of the greatest masters of 20th century art into a truck and headed west.

As the Soviet army approached from the east, he drove for two days along bomb-cratered roads into the hill country of northern Bavaria. His destination was a castle called Schloss Aschbach, where the local baron agreed to shelter Mr. Gurlitt's family and his art.

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