MOSCOW—He operated under cover with a single false name on two continents for 34 years, through part of the Cold War and beyond. He served spymasters in Moscow who reward such steel-jawed endurance with quiet adulation.

In Peru he was Juan Lazaro the karate black belt, the news photographer, the guy who married the star TV reporter. After the couple moved to New York, he became Juan Lazaro Ph.D. and adjunct professor of political science. At home in suburban Yonkers, he was the doting father of Juan Lazaro Jr., a talented young pianist.

A Spy's Life

No one suspected until he was arrested by the Federal Bureau of Investigation, unmasked as Mikhail Vasenkov and sent home in the much-publicized U.S.-Russia spy swap a month ago.

Prime Minister Vladimir Putin feted the 10 deported agents, including femme fatale Anna Chapman, led them in patriotic Soviet songs and promised them decent jobs and a "bright life" in the motherland.

But the senior spy among them says no thanks. In a plot twist rare in the annals of espionage, he wants his Juan Lazaro fake identity back.

There's only one problem. The real Juan Lazaro died 63 years ago in Uruguay at age 3, a relative says. The spy used the dead toddler's birth certificate to build a persona.

From a Moscow apartment where Russia's government has him lodged out of public view, the veteran agent has sent word that he and his wife, deported together in the spy swap and separated from their 17-year-old son, want to use their Peruvian passports to return to Peru in the coming weeks and rebuild their lives as the Lazaros.

"He doesn't want to stay in Russia," says his American lawyer, Genesis Peduto, who talks to him on the phone.

"He says he's Juan Lazaro and he's not from Russia and doesn't speak Russian. He wants to be where his wife is going, to her native country, where it will be easier for Juan Jr. to visit" from New York. "His family comes first."

Ms. Peduto says she has no knowledge of the dead Juan Lazaro and won't comment. Her client declines to be interviewed. Russia's Foreign Intelligence Service refuses to comment on any of the 10 deported agents.

The spy ring puzzled Americans and tested U.S.-Russian relations. It was an odd group: They included four couples with children living suburban lives while secretly sending radiograms, exchanging bags of cash in "brush passes" and delivering messages in invisible ink.

They seemed to be looking in hidden places for data that were largely available on the Internet. Watched for a decade by the FBI, they managed to obtain no classified data, U.S. officials say.

The Juan Lazaro story is a peculiar footnote. The spy's early life remains a mystery. But his paper trail through Spain, Uruguay, Peru and New York offers a glimpse into the world of Moscow's "illegals," or deep-cover agents, and its Hispanic pipeline to America. In that realm of forgery, identity theft and deception within families, it remains unclear whether the spy's wife and collaborator, Vicky Pelaez, even knew of his other name.

Soviet and Russian deep-cover agents have spent years at a time in the U.S. since early in the Cold War, operating without diplomatic cover or immunity from prosecution. Many lived in Peru during the country's rule by Moscow-friendly military officers in the 1970s, building fake identities before infiltrating the U.S., former KGB officials say.

Successful illegals return to waiting families, Kremlin rewards and prior Russian identities.The Lazaro case appears to be that of a loyal but ineffectual agent who operated so long under cover that he became his fictional self—a make-believe Latino who went native.

"He ceased being Russian, it seems, and began thinking of himself as Juan Lazaro," says Boris Volodarsky, a former Soviet intelligence officer who works in London as an independent analyst.

The persona took shape on March 13, 1976, as a man with a droopy mustache flew from Madrid to Lima, Peru, on a Uruguayan passport in the name of Juan Jose Lazaro Fuentes.

He bore a letter on a Spanish tobacco company's stationery saying he had been hired for a market survey in Peru, according to a file kept by the Peruvian Interior Ministry on his citizenship application.

Juan Lazaro, in striped sweater, poses with Peru's president in 1981. Carlos Saavedra Soria

Two years later, he submitted copies of the passport and a 1943 Uruguayan birth certificate with a letter asking Peru's military dictator to make him a citizen of "the most humanist country" in Latin America. The letter, short on detail, said he lived in Uruguay until age 7, then left to study and work in Spain.

Mr. Lazaro spoke Spanish with a Slavic accent but "never talked about his past," recalls Delfina Prieto, a journalist who worked with him in Peru. After a cursory background check, Peru gave him citizenship in 1979.

In 1983, he married Ms. Pelaez. Two years later they moved to New York with her son from a previous relationship. She became a columnist for El Diario, New York's Spanish-language daily, got U.S. citizenship and gave birth to Juan Jr. At home they spoke Spanish. Juan Sr., a legal U.S. resident, earned a doctorate in political science at the New School.

"I didn't detect anything odd," says Thomas Halper, who hired him to teach at Baruch College, of the City University of New York. "His preoccupation was with his son. He seemed so dedicated to his son, so proud of him."

His story unraveled after the couple's June 27 arrest.

The FBI reported a bugged conversation in the Lazaros' Yonkers home in which Mr. Lazaro said his family moved to Siberia about the time he was born.

The FBI alleged that the couple traveled from New York to South America several times over the past decade to receive cash from Russian operatives and deliver messages, although it recorded Mr. Lazaro complaining, "They say my information is of no value."

He, his wife and the eight others pleaded guilty as part of the spy-swap deal. Defense lawyers say he gave the name Russian officials told him to give—Vasenkov—reading it in court from notes.

And who is Vasenkov? Former KGB officials say that name may be no more genuine than Lazaro is. A search of Russian directories and websites turns up no Vasenkov fitting the profile. "The guy may have had several names," says Oleg Kalugin, a former general who once ran KGB operations in the U.S.

Whatever his real name, the spy apparently forged that tobacco company assignment letter. Altadis SA, the company's current owner in Madrid, says it found no record of a Juan Lazaro in its files.

The spy left one trace of his Lazaro identity in Spain: a brief stay on a three-month visa in early 1976 on his way to Peru, according to stamps in his Uruguayan passport.

Peru is investigating whether he committed fraud to obtain citizenship. Uruguayan officials aiding the probe say anyone with knowledge of the real Juan Lazaro's identity could have appropriated his birth record.

That's apparently what happened in this case. In Uruguay, Elida Panizza Fuentes told the Journal that Juan Lazaro was her half-brother. She says he died of respiratory failure in 1947.

Eva Irene Fuentes is listed as the child's mother on the birth certificate used by the spy. A widow, she remarried and gave birth to Ms. Panizza in 1948. Before her death, the mother told Ms. Panizza the story of the sickly boy the family remembered as "Juancito."

"She couldn't help crying whenever she spoke of the child," Ms. Panizza says. She says it saddened her to learn a spy had taken his identity. "How could they do something like that?"

Ms. Pelaez asked her own pointed question. She confronted her husband in a holding cell as they awaited deportation and, according two lawyers present, demanded: "What's your name? Your real name."

Carlos Moreno, her lawyer, says her husband laughed and replied, "My name is Juan Lazaro." The lawyer said the two are standing by each other and the Lazaro name. He added: "My guess is she didn't know him as anyone else."

—Robert Kozak and Sophie Kevany in Lima, Peru; Santiago Perez in Madrid; Diego Fischer in Montevideo, Uruguay; and Jonnelle Marte in Yonkers, New York, contributed to this article.

Write to Richard Boudreaux at richard.boudreaux@wsj.com