HAVANA, Cuba (CNN) -- An American couple who allegedly kidnapped their two sons and sailed to Havana last week sat in a Florida jail Wednesday after Cuba hastily handed them over to U.S. officials.
Cuban authorities turned over the family of four to the U.S. State Department and the FBI after CNN found them in Havana on Tuesday.
They arrived in Florida early Wednesday, where the two boys, ages 2 and 4, will get a medical exam, according to Hillsborough County Sheriff David Gee.
He said they secured the family dog for the boys, who will be reunited with it later.
Authorities booked the parents, Josh and Sharyn Hakken, into the county jail. They face federal and multiple state charges, including kidnapping, auto theft and child neglect.
The couple is being held in Tampa, away from the general population but without special treatment, said Cpl. Howard Lindsey of the Hillsborough County Department of Detention.
Chase, 2, and Cole, 4, will live in Florida with their maternal grandparents, Bob and Patricia Hauser. They have had legal custody of the boys since a court in Louisiana terminated the couple's parental rights this month, Gee said.
"Our grandchildren are safe," said Bob Hauser, who spoke with them before they departed Cuba. He thanked the Cuban government "for being so cooperative and returning the kids."
The United States Interests Section in Havana, Cuba, praised Cuban officials for their handling of the case.
"We would like to express our appreciation to the Cuban authorities for their extensive cooperation to resolve this dangerous situation quickly," spokeswoman Lynn W. Roche said in a statement.
CNN found the Hakkens in Havana
CNN found Josh and Sharyn Hakken hunkered down with their two toddlers in a sailboat at the Hemingway Marina in Havana on Tuesday.
Theirs was no ordinary visit to the historic port, where they had briefly eluded capture. The Hakkens have been on the lam after they allegedly snatched the two boys from the Hauser home in Florida.
Josh Hakken allegedly entered the Hauser home a week ago, tied up the boys' grandmother then fled with the children in her silver 2009 Toyota Camry. That vehicle was later found a couple of blocks away from the home.
Florida investigators told CNN they believe Hakken joined up with his wife. The two boarded a sailboat in nearby Madeira Beach.
Surveillance images showed the boat sailing into the Gulf of Mexico about three and a half hours after the boys disappeared from their grandparents' home, investigators said, adding that the photos showed adults and children on board.
Cuban officials quickly announced Tuesday afternoon that they would turn the family over to U.S. authorities.
In the port, Josh Hakken glared through his sunglasses at the CNN reporter who found him and said nothing beyond confirming his identity.
The two boys are OK, said a woman matching the description of his wife. She left it at that.
Cuban security had an eye on them
Cuban security officials wearing sidearms appeared as the CNN crew was filming and ordered it to stop.
At the security guards' request, CNN stepped away from the boat, which resembled a photo circulated by Florida law enforcement officials, except more battered.
A statement from the Cuban Foreign Ministry said the boat pulled into the marina, a few miles west of Havana, in bad weather Sunday.
"From the first moment, diplomatic notes were exchanged and a permanent and professional communication has been maintained between MINREX" -- the Cuban Foreign Ministry -- "and the U.S. Interests Section in Havana, with the goal of guaranteeing the integrity and well-being of the minors," the statement said.
U.S. government officials have told the sheriff's office in Hillsborough County, Florida -- which includes the city of Tampa from which the boys went missing -- that they received "exceptional cooperation from the Cuban government," the sheriff's office said Tuesday afternoon.
The Hakkens and the law
The Hillsborough County Sheriff's Office described Josh Hakken as an anti-government protester, and he was believed to be armed.
Last week, police in Slidell, Louisiana, issued a statement offering background on the Hakkens and why the boys were taken from the parents last year.
In June, Slidell police responded to a disturbance report at a hotel where Josh and Sharyn Hakken were staying with their sons, the police statement said.
"When police arrived, both Mr. and Mrs. Hakken were acting in a bizarre manner that alarmed officers. They were talking about 'completing their ultimate journey' and were traveling across the country to 'take a journey to the Armageddon'," the Slidell police statement said, adding, "Let it be noted that both of their children were present in the hotel room at the time."
Because of the parents' behavior and "the fact that narcotics and weapons were located inside of the hotel room," the children were taken by child welfare officers, and Josh Hakken was arrested on drug charges, the statement said.
State and federal charges
He and his wife face a federal charge of unlawful flight to avoid prosecution, Gee said. The state is charging both with kidnapping, interference with child custody, child neglect, battery and grand theft auto. Josh Hakken faces an additional charge of false imprisonment.
There is no extradition treaty between Cuba and the United States, although there have been recent cases in which Americans sought for crimes in the United States and discovered in Havana have been sent back by the Cubans.
The FBI estimates there are 70 fugitives from U.S. justice in Cuba, which is one of the reasons it remains on the U.S. list of countries that support state terrorism. Most of the American fugitives in Cuba have been there for decades and have ties to revolutionary movements or radical groups.
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