A Stradivarius which belonged to renowned violinist Roman Totenberg has been recovered after 35 years.

Totenberg left the violin in his office while greeting well-wishers after a concert in 1980 but when he returned it was gone.

Its case was later found in the basement of the Longy School of Music in Cambridge, Massachusetts, where he taught. But Totenberg, who died three years ago aged 101, never saw the instrument again.

Totenberg thought he knew who stole the violin, but there was never enough evidence to pursue a suspect.

The trail went cold until this June, when his eldest daughter, Nina Totenberg, got a phone call from an FBI agent.

The agent said he was looking at the violin, which was in federal custody.

“I really could hardly believe it at the time,” Nina Totenberg said.

The violin, known as the Ames Stradivarius, was made in Italy in 1734 by Antonio Stradivari and is one of roughly 550 Stradivarius instruments known to exist.

They can fetch millions of pounds at auction, including a record $15.9 million in 2011.

The violin surfaced in June when a woman brought it to New York to have it appraised. The appraiser, Phillip Injeian, immediately contacted authorities. He said the violin has characteristic markings on the wood grain that are “like a fingerprint”.

“It’s really one of a kind,” Injeian said at a news conference in Manhattan, where authorities announced the recovery of the violin. “When I saw this one, it was a Eureka moment.”

The woman who sought the appraisal is the former wife of Philip S Johnson, who died in California in 2011. She declined to comment and has not been accused of any wrongdoing.

According to court documents, the woman voluntarily returned the violin to the Totenberg family and told investigators she did not know it was stolen. It had been stored for many years in a case with a combination lock.

US attorney Preet Bharara said there was “no open investigation” related to the violin’s disappearance.

Johnson’s obituary described him as “a noted violinist of 40 years” but did not detail where or for whom he played. Totenberg said he was an aspiring violinist seen around her father’s office at the time of the theft.

Totenberg said that, lacking evidence, police were not able to obtain a warrant to search for the Stradivarius.

“There was nothing to be done, and eventually he just moved on and bought another violin and lived the rest of his life,” she said.

A child prodigy in his native Poland, Roman Totenberg bought the Stradivarius in 1943 for $15,000 – more than $200,000 in today’s money – and it was the only instrument he performed with until it was stolen. He kept performing into his 90s and taught at Boston University until he died.

The story of its theft and recovery is not uncommon for Stradivarius instruments, which are virtually impossible to sell on the black market. Injeian said there are about 20 Stradivarius instruments currently known to be stolen.

Another famous Stradivarius, the Gibson, was stolen in 1936, and the thief, a journeyman violinist, confessed on his deathbed in 1985. It is now owned by violinist Joshua Bell.

A Stradivarius violin belonging to Erika Morini was stolen from her New York flat in 1995 by someone who had a key to the locked bedroom wardrobe where she kept it. Morini was not told about the theft before she died weeks later. The instrument has never been found.

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