"The application has been submitted to the court. The court will decide," Prosecutor Rozita Požarskienė told BNS on Wednesday.
The Vilnius Regional Court has scheduled a hearing on the extradition request for Friday.
The BBC has reported that Google and Facebook have confirmed that they fell victim to an alleged 100-million-dollar scam orchestrated by Rimašauskas.
The request for extradition reached Lithuania on April 18 via diplomatic channels. The Foreign Ministry received the request from the US embassy in Lithuania and forwarded it to the Prosecutor General's Office.
The prosecutors are asking the court to extradite Rimašauskas based on an international extradition treaty with the US, as well as national laws.
The 48-year-old suspect was detained on March 16. A Vilnius court then issued a one-month arrest warrant, which was on April 13 extended for another month.
US law-enforcement officials have brought fraud, money laundering and identity theft charges against the Lithuanian citizen.
The US Department of Justice has said in a press release that Rimašauskas orchestrated the fraudulent scheme between 2013 and 2015.
"From half a world away, Evaldas Rimašauskas allegedly targeted multinational internet companies and tricked their agents and employees into wiring over $100 million to overseas bank accounts under his control," it quoted Acting U.S. Attorney Joon H. Kim as saying.
He said that much of the stolen funds had been returned to the US companies.
It is said that Rimašauskas registered a company in Latvia that had the same name as an Asian-based computer hardware manufacturer and held several bank accounts in the neighboring country in the name of that company.
"Fraudulent phishing emails were sent to employees and agents of the victim companies, which regularly conducted multimillion-dollar transactions with (the Asian) company," the Department of Justice said.
According to the department, these emails purported to be from employees and agents of the Asia-based company and were sent from email accounts designed to look like they had come from that company.
"This scheme succeeded in deceiving the Victim Companies into complying with the fraudulent wiring," it said.
After the funds were transferred, Rimašauskas "caused the stolen funds to be quickly wired into different bank accounts in various locations throughout the world, including Latvia, Cyprus, Slovakia, Lithuania, Hungary, and Hong Kong".
The Lithuanian man is also suspected of forging invoices, contracts and letters "that falsely appeared to have been executed and signed by executives and agents of the victim companies (...) to be submitted to banks in support of the large volume of funds that were fraudulently transmitted via wire transfer".