The Justice Department moved Monday to strip citizenship from four Somali immigrants who prosecutors say lied about being a family, defrauding the Diversity Visa Lottery program that Republicans are aiming to nix.

The government says one woman, Fosia Abdi Adan, won the visa lottery in 2000 and then illegally brought in three cousins, claiming two were her children and one was her husband — even though the man was married to another woman at the time.

The fake couple quickly filed for divorce and the bogus husband later tried to bring his real wife and children to the U.S., investigators said in court documents.

Nearly a decade after the scam was revealed, the Trump administration is now taking action to revoke their citizenship, filing papers in U.S. District Court in Minnesota.

The move comes a week after the Diversity Lottery was in the news as the immigration program used by the Uzbekistan-born suspect in last week’s terrorist truck attack in New York City.

“The current immigration system is easily abused by fraudsters and nefarious actors, and that’s certainly true of the Diversity Immigrant Visa Program,” Attorney General Jeff Sessions said in announcing the actions.

Mr. Sessions said that because of the fraud, Ms. Adan was successfully able to bring three people to the U.S. illegally — and court documents said a half-dozen other people tried to immigrate connected to the fraud but were stopped.

The visa lottery doles out about 50,000 visas a year based on pure chance. Designed in 1990, the program was intended to give immigrants from countries that didn’t have a large U.S. population a means of entry.

Recently, however, Republicans — and some Democrats — had said the program had outlived its usefulness and had become a liability, particularly because of fraud.

The full extent of fraud in the program isn’t known, but snapshot investigations have given indications, including a 2013 State Department inspector general’s report finding “widespread fraud” in the lottery program in Ukraine.

Organized crime rings had taken control of the program, entering people’s information without them knowing it, and if they won, the crime syndicates would then pay thousands of dollars to bully the people into agreeing to a sham marriage to get someone else into the U.S. on the same golden ticket.

Ms. Adan’s case also involved marriage fraud.

Investigators said in court that when she applied for the lottery, she claimed to be married to a man named Jama Solob Kayre and produced a fake marriage license. They also claimed to have three children: Mohamed Jama Solob, Mobarak Jama Solob and Mostapha Jama Solob — names created specifically to create more spaces to claim diversity visas.

But all of them were actually cousins, and the man who claimed to be her husband, Ahmed Mohamed Warsame, was married to another woman who was pregnant with his son at the time.

The cousins all submitted false names in their applications pretending to be Ms. Adan’s immediate family.

“This example is not uncommon at all,” said Matthew J. O’Brien, director of research at the Federation for American Immigration Reform and a former anti-fraud official at U.S. Citizenship and Immigration Services. “People regularly sell spots and the highest bidder in their locality becomes their husband, the next highest bidder becomes child No. 1.”

In the case of Ms. Adan, while two of her cousins were admitted as her children, the third “child” was blocked.

Still, Ms. Adan, the fake husband and the other two fake children all applied for and were granted citizenship.

A year after Ms. Adan and her false husband arrived in the U.S. they got a divorce. Mr. Warsame, the bogus husband, then tried to bring his real wife, Yurub Jama Hirad, and their four actual children to the U.S.

Mr. Warsame went through name-changes, created a fake first husband for his actual wife, and claimed his children were actually stepchildren to try to explain away the fake marriage to Ms. Adan, investigators said.

USCIS actually approved immigration petitions for some of Mr. Warsame’s family but the story began to unravel when they appeared for an interview at the U.S. embassy in Yemen.

DNA samples were taken in 2010 and the results further exposed the fraud. For some reason investigators didn’t pursue the fraudsters in the U.S. until last year.

Mr. O’Brien said the government should have lodged criminal charges against the four, instead of only moving to strip their citizenship.

He also said the government could have stripped citizenship administratively rather than gone to the courts, which could have been a faster option.

“The DOJ has become infested with people that think once you become a citizen, stripping that citizenship is a huge civil rights issue,” he said.

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