Prosecutors say Teixeira leaked classified documents to a group of gamers on the messaging app Discord.
Teixeira is accused of committing one of the most serious US security breaches since more than 700,000 documents, videos and diplomatic cables appeared on the WikiLeaks website in 2010.
The recording shows Trump, who is seeking the 2024 Republican presidential nomination, understood he retained classified material after he left the White House in 2021.
The suspect leaked the season finale of the "Game of Thrones" spin-off two days before it was set to release in October.
The materials posted online offered a partial, month-old snapshot of the war in Ukraine.
In my opinion, this matter has undisclosed facets, and a considerable portion of it will remain confined within the classified US archives.
"The damage the defendant has already caused to the US national security is immense. The damage the defendant is still capable of causing is extraordinary," the memo says.
New documents from the leaked Pentagon papers suggest that the rounds of sanctions did have an impact on Russia, but didn't cripple it.
Ukraine's medium air defenses would be inert by May 23, shifting reliance to lower-layer air systems.
A conviction on the Espionage Act charge carries up to 10 years in prison.