Google sought to block the order to give up the emails this week on the basis that to do so would infringe Mr Akhmedov's right to privacy because he had not given consent to share them.
Ms DeMarchi said Google's concern for the "privacy and security of its account holders' communications" was "commendable" but ruled the request did not breach the US Stored Communications Act, which governs voluntary and compelled disclosure of emails.
Google was ordered to produce all emails, documents and other information connected to two email accounts and preserve the accounts for 90 days.
The order comes days before the Akhmedovs are due to face each other in the High Court in London over the blockbuster settlement. The sum was awarded in 2016 by the High Court, but Mr Akhmedov senior claims it was superseded by their divorce in Moscow 20 years previously.
Ms Akhmedova brought her son into the dispute last year when she accused him of helping her ex-husband to hide assets from her in order to avoid paying the court award. Her son, a commodities trader based in London, has since had his property raided after a UK judge accused him of destroying critical documents as part of the divorce case.
Lawyers for Ms Akhmedova were seeking items including a desktop computer, laptop, mobile phone and Apple Watch, all of which her son claimed to have lost in transit between France and London.
Some 58 devices were ultimately recovered — 47 apparently belonging to Temur Akhmedov — which Mrs Justice Knowles said "appear to have been actively concealed from the wife, this court and Temur's former solicitors".
In a statement on Wednesday a spokesperson for Temur Akhmedov called the exercise "futile" and said the seized devices included an old PlayStation and children's Peppa Pig computer game belonging to his four-year-old daughter.
"As a result of this latest Google hearing, Temur hopes his mother and her backers will enjoy reading the contents of his old High School email account," the spokesperson said.
"This case and ruling are the latest evidence of the desperation of Tatiana and Burford Capital's to find 'evidence' against him which simply does not exist," the spokesperson said. Temur has nothing to hide despite his mother's and Burford Capital's "vastly expensive wild goose chase around the world's courts", the spokesperson added.
- Financial Times