Even as the United States fought the Axis Powers in Europe, Africa and Asia during World War II, a new threat emerged at home — this time from a Nazi spy ring operating out of South America.

The cell sought to conduct both political and military operations as they worked to sway the politically-neutral continent towards the Germans, while reporting on Allied ship movements, putting vessels at risk of destruction by German U-boats.

J. Edgar Hoover’s FBI had no answer for the ring. But Elizebeth Smith Friedman did.

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Working for the Coast Guard under the Treasury Department, the veteran codebreaker (whose Jewish-American husband, William Friedman, was himself a legendary name in intelligence history) had honed her skills battling Prohibition-era smugglers — who, it turned out, had used codes similar to those employed by the Nazi spies.

Friedman not only cracked the Nazi codes, she helped bring down the spy ring. In January 1944, Nazi isolation from South America was complete when Argentina broke off relations with the Axis.

Yet for decades, this story — and the woman behind it — were lost to history.

Now, a new book, “The Woman Who Smashed Codes: A True Story of Love, Spies, and the Unlikely Heroine Who Outwitted America’s Enemies” by Jason Fagone, aims to correct this oversight.

It comes on the heels of the 2014 movie “The Imitation Game” — about Friedman’s British codebreaking contemporary, Alan Turing — and this year’s film “Hidden Figures,” about African-American women in the space industry who were also ignored by history.

“You go back and look at public sources, and women are there,” Fagone said. “They’ve been there all along. They were omitted from the story when the story got told by men, sometimes even outright erased. Elizebeth and her WWII heroics were papered over by J. Edgar Hoover. All the while, Hoover claimed credit for what Elizebeth and her team were doing.”

Fagone discovered her story several years ago. He was researching the National Security Agency (NSA) while reporting on Edward Snowden, who leaked information from the agency in 2013.

The author began reading about William Friedman, whom he said “was considered the godfather of the NSA,” and was also renowned for breaking the Japanese WWII Purple code.

“I noticed his wife was also a codebreaker,” Fagone said. “I thought, ‘that’s interesting, husband and wife codebreakers.’ … I got curious and began to dig. It was this kind of incredible untold story, a woman at the heart of the American intelligence community, that began to unfold.”

She was born Elizebeth Smith to Quaker parents in Huntington, Indiana, in 1892. Her mother Sopha provided her unconventional first name.

She had an early interest in codes — including a belief that the works of Shakespeare contained secret messages. George Fabyan, a Gilded Age tycoon from Chicago, recruited her to try to find these messages — one of his many projects.

Smith also met a geneticist on Fabyan’s staff named William Friedman — a Russian immigrant born as Wolf Friedman, the son of a Talmudic scholar.

“William was interested in a homegrown version of Zionism,” Fagone said, although later in life he criticized the movement.

“As a young man growing up in Pittsburgh, he decided at an early age he was going to try to learn being a farmer. His high school friends believed Jewish youths needed to make themselves strong in the face of anti-Semitism and go back to the land. Ultimately, he decided to become a scholar of genetics instead,” said Fagone.

Friedman and Smith married in 1917. “It was not something that was really done in their worlds,” Fagone said. “She was a Quaker girl from the Midwest, Friedman was from a Jewish community in Pittsburgh.”

But, he said, “Young people in love, as often happens, their love for each other was stronger than fears of what their families would think.”

They would have a lasting marriage, with two children. Codebreaking kept them close.

“They were two young people who wanted to accomplish very great things,” Fagone said. “They clicked through this very intense activity of codebreaking. They would be across the table from each other, for eight, 10, 12 hours a day, cranking through puzzles. They loved it.”

They became highly successful at it. “William Friedman, like Elizebeth Friedman, was one of the great codebreakers of all time, a genius at seeing patterns in what looked like noise,” said Fagone. “Along with Elizebeth, he was involved in some of the methods at the foundation of modern cryptology.”

When America entered WWI in 1917, “very quickly, because of the necessities of war, [Elizebeth Friedman] was transferred from the Shakespeare project to hunt and solve secret messages to Germany,” he said.

Her husband went to France in 1918 as a codebreaker for the American Expeditionary Force. Throughout his career, however, he faced anti-Semitism.

“He grew up hearing stories of anti-Jewish pogroms that had swept through the family’s ancient home in Russia,” Fagone said. “Those stories never left him. I think, all his career, he was aware of anti-Semitism in the US military. He was afraid it would harm his career and livelihood.

“The US military was thoroughly anti-Semitic, in a casual, everyday way. … People he worked with in the War Department believed in anti-Semitic frauds, gathering intelligence about what they called ‘the Jewish question’ on MID [Military Intelligence Division] index cards. One was called ‘Jews: Race.’ That was the professional environment of William Friedman,” said Fagone.

Meanwhile, Elizebeth Friedman would make history at “the only codebreaking unit in America ever to be run by a woman,” Fagone wrote.

Working for the Coast Guard under the Treasury Department of Henry Morgenthau Jr., “she battled smugglers and professional gangsters, intercepting messages, literally reading the thoughts of the biggest gangsters of the day,” Fagone said. “She testified, sometimes at risk to her personal safety.”

The couple’s interwar achievements helped them accomplish great feats during WWII. William Friedman led the Army team that cracked the Japanese code Purple.

“Ultimately, they were able to intercept, break and read Japanese diplomatic messages all through the war,” Fagone said. “They read into the minds of top Japanese diplomats all over the world — and also the Nazi mind. Japanese diplomats were talking with their Nazi counterparts. William and his team read that, too. In an enormous way, they probably helped shorten the war.”

However, Friedman suffered a nervous breakdown and was honorably discharged.

“Later in life, when his depression became more acute, he talked about the toll that anti-Semitism was taking on him with a psychiatrist,” Fagone said.

And while he helped create what became the NSA in 1952, Cold War-era tensions arose between the Friedmans and the agency, boiling over in 1958, when agents removed many of the Friedmans’ personal papers from their Capitol Hill home.

While William Friedman’s wartime achievements are well-known, his wife’s are not. Of the 22 boxes of personal files Elizebeth Friedman left to the George C. Marshall Foundation library in Virginia, there was no documentation between 1939 and 1945.

It turned out that her records had been declassified in 2000. Locating them in the National Archives “was the part that took me the most time and research,” Fagone said.

It took two years, and “it was more dramatic and surprising than anything I had ever expected.”

Elizebeth Friedman had matched wits with Johannes Siegfried Becker — “the most prolific and effective Nazi spy in the Western Hemisphere during WWII,” Fagone wrote.

Becker’s spy network in South America collected intelligence that “would allow a U-boat to go after an Allied vessel,” Fagone said. “A Nazi spy in Buenos Aires or another port would note when an Allied ship would depart at a certain time. Berlin would dispatch a U-boat that would attempt to destroy it with a torpedo. … It was a death warrant. There were dozens, hundreds of people aboard an Allied vessel. It was important to be able to intercept, warn the captains.”

Other intelligence “gave Germany a picture of what goods were being transported to whom,” Fagone said.

“A lot of espionage was about commerce, raw materials, ores, food to feed the army. Various South American governments made deals with both sides to secure a line on imported ores, metals, supplies of food. It was useful to know if a ship full of Argentine beef was heading in a certain direction,” he said.

These messages were transmitted via clandestine radio networks.

“For anyone to find out what they were saying, they had to intercept the radio messages and break the codes,” Fagone said. “The FBI was totally unprepared. They had no codebreaking team.”

But the Coast Guard and Elizebeth Friedman were perfectly prepared. “Elizebeth had built an elite team of codebreakers within the Coast Guard,” Fagone said.

“The Nazi spies had very similar radio techniques, very similar codes, to the rum runners and drug smugglers in the 1920s, 1930s. It just shows how Elizebeth was ready, with that sort of skills, for a pivotal moment in the war. … She shifted her focus from fighting smugglers to tracking and hunting spies all through WWII,” he said.

Decades later, the NSA was skeptical of the threat from Nazi spies in South America.

“Did the Axis’ clandestine effort in the Western Hemisphere have any effect on the conduct of the war? Probably not,” David P. Mowry wrote in a since-declassified 1989 publication, “German Clandestine Activities in South America in World War II.”

“It appears that most of the intelligence passed to Germany was of little significance,” said the article. And “[The] answer to the question, ‘Did the US cryptanalytic effort against the Axis spies have any effect on the conduct of the war?’ is also, ‘Probably not.’”

However, Friedman and her team made an impressive 4,000 decryptions from 50 separate Nazi radio circuits.

Fagone said the decriptions managed “to create a detailed map of the Nazi spy network in South America … figure out who was talking to who and why, map connections with various South American governments to track finances down to the peso, learn code names and true identities of all agents” — all of which helped authorities “go in and disrupt, arrest and destroy spy networks, eliminate the Nazi espionage threat.”

She also assisted with high-profile domestic espionage cases. “Her role was omitted or erased when the FBI told the story,” Fagone said.

She and her Coast Guard team decrypted intelligence that aided Hoover’s 1941 investigation of the Duquesne spy ring — in which 33 men went to jail for a collective 300 years.

In 1944, she testified as an expert against Japanese spy Velvalee Dickinson, nicknamed the Doll Woman for writing letters purportedly about sales from her New York doll shop that actually described damage to Allied warships.

“The FBI did a lot of good work in WWII,” Fagone said, “in the Duquesne case, and a lot of good work with the Doll Woman. It’s just that, when [Hoover] told the story, the FBI did everything.”