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A US man who faked his own death and fled the country, leaving behind his family, has sent investigators in his home state of Wisconsin a video to prove that he is safe.

Ryan Borgwardt, 45, vanished on 12 August while on a solo fishing trip, the Green Lake County Sheriff's Office said in a news conference on Thursday.

Police initially suspected that he had drowned and searched the lake for 54 days, before finding digital evidence that led them to suspect he had fled to Eastern Europe.

The authorities said Mr Borgwardt owes them $40,000 (£32,000) for the cost of their search and could be charged with obstructing the investigation into his disappearance.

Green Lake County Sheriff Mark Podoll told a press conference on Thursday that the authorities had been in contact with Mr Borgwardt since earlier this month, after contacting a woman who speaks Russian.

She helped connect him to police. Law enforcement did not detail who the woman was or her connection to Mr Borgwardt.

"The great news is he's still alive and well," Mr Podoll said. “The bad news is that we don’t know where exactly Ryan is, and he has not decided to return home.”

The 24-second video that Mr Borgwardt sent to the authorities is shot selfie-style, and shows him in an apartment with white walls.

“Good evening, it’s Ryan Borgwardt,” he says. “Today is 11 November. It’s approximately 10 am by you guys. I’m in my apartment.

"I am safe, secure, no problem. I hope this works.”

During their near-daily exchanges, Mr Borgwardt allegedly revealed to police how he orchestrated his getaway.

Police say that after sinking his kayak and mobile phone in the lake, he paddled a small child-sized boat to shore where he had stashed an E-bike. He cycled overnight to Madison, Wisconsin, then boarded a bus to Detroit and got on a plane in Canada to an unknown location.

“We are continuing to verify this information, trying to put the dots together,” Mr Podoll said. “But we feel that this was Ryan’s way that he could tell the entire country how he did it.”

Mr Borgwardt is thought to have acted alone. Mr Podoll added that he has not had any contact with his family since he left.

He left behind three children and his wife. In the days before his departure, authorities found he had taken out a $375,000 (£297,875) life insurance policy, had transferred funds to a foreign bank account, photographed his new passport, and altered his email address. He had also been in contact online with a woman in Uzbekistan.

When asked about his possible motivation for faking his own death, Mr Podoll said "he just had personal matters going on and he thought this was the right thing to do".

He added that police have been emailing Mr Borgwardt, "pulling at his heartstrings" in an effort to coax him back home and “clean up the mess that he has created”.

The sheriff became emotional during Thursday's press conference, saying that his children will be without their father during the holiday season.

"Christmas is coming up," he said. "And what better a gift to give those kids than to be there for Christmas."