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He faced trial in Los Angeles after the FBI raided a property and arrested him.
The 37-year-old Nigerian, who is thought to have used email scams to amass his considerable wealth, was found with £29m in cash and 13 luxury cars.
The court documents show that the footy club was one of the targets of a business email compromise swindle, through which legitimate email accounts are hacked and then spoofed.
Abbas has also been accused of money laundering.
The criminals attempted to get the Premier League team to part with £100m back in 2019, but the United States Attorney's Office has refused to name the club or to confirm whether the money was actually handed over.
Another business in the UK was scammed out of £200m and thousands more are thought to have been involved in the worldwide con.
Hushpuppi is known for his extravagant lifestyle and had amassed a large number of followers online, including 2.5 million Instagram followers.
The acting United States Attorney General Tracy Wilkinson said that Abbas and his criminal companions tried to steal more than $1m from someone who wanted to fund a new school in Qatar by 'playing the roles of bank officials and creating a bogus website'.
She added that they 'bribed a foreign official to keep the elaborate pretence going after the victim was tipped off'.
He will have to 'pay full restitution to the victims' for his crimes.
Wilkinson said that Abbas 'played a significant role' in the scam, which 'funded his luxurious lifestyle by laundering illicit proceeds generated by con artists.'
Kristi Johnson, the acting director of the FBI's Los Angeles office, described Abbas as one of the 'most high-profile money launderers in the world'.
She added that his 'celebrity status and ability to make connections seeped into legitimate organisations and led to several spin-off schemes in the US and abroad'.
His guilty plea, she said, represents 'a crucial blow to this international network'.
When sentenced, he could be looking at as many as 20 years' imprisonment.
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