Police may be on the brink of finding the remains of Judge Joseph Crater and possibly solving the most enduring mystery in New York City...

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NEW YORK — Police may be on the brink of finding the remains of Judge Joseph Crater and possibly solving the most enduring mystery in New York City history, investigators say.

A letter probably penned more than 50 years ago has pinpointed a spot under the Coney Island boardwalk where Crater — last seen leaving a Times Square watering hole 75 years ago — is buried, they said.

The letter was written by a woman who died of natural causes in June, they said.

Upon her death, family members opened a safe-deposit box, where granddaughter Barbara O’Brien found a letter with “Do Not Open Until My Death” instructions on the envelope.

In it, the letter writer wrote that her father told her on his deathbed where Crater’s remains were — on the current site of the New York Aquarium — and that cab driver Frank Burn was his killer.

The names of the letter writer and her father are being kept secret.

O’Brien’s phone rang unanswered yesterday at her Long Island home.

Detectives said everything the woman wrote so far has been corroborated.

For generations, Joseph Crater — a Tammany Hall stalwart, justice of the state Supreme Court and dapper man about town — has been what some newspapers have called “the most missingest man in America.”

His baffling disappearance spawned thousands of jokes and from time to time rumors circulated of him being spotted on a South Sea isle or in some other remote locale. Long before Elvis, Judge Crater sightings were an international phenomenon. There were reports of Crater in a Manhattan nightclub, a Maine cottage, of Crater wandering through Havana, of playing bingo in North Africa.

Appointed to the trial-court bench by then-New York Gov. Franklin Roosevelt, Crater, 41, had been a judge for four months when he vanished.

On Aug. 6, 1930, he cashed two checks amounting to more than $5,000 and took along an additional $20,000 in campaign money — equal to about $250,000 today.

He packed up files in his office and, as he left , told his assistant, “Don’t forget to turn out the lights, Johnson.”

That evening, the tall, 200-pound judge, with slicked-back, graying hair parted down the middle, dined with his showgirl mistress and another friend.

After dinner, “Good Time Joe” — his moniker because he loved to dance — hailed a cab, waved his straw Panama hat out the window and vanished.

A grand jury called 95 witnesses and amassed nearly 1,000 pages of testimony but never learned what happened to him.

Some have speculated he was rubbed out by — or at the request of — his girlfriend’s other boyfriend, a mobster.

Two months after Crater vanished, the girlfriend also disappeared.

Others have long suspected that mobster Frank Costello offed Crater as payment to Tammany Hall politicians who were protecting his rackets.

Still others believed Crater was killed because he was about to expose corruption in Tammany Hall.

Material from The Associated Press is included in this report.