Oh silly one, Obama turned ALL OF HIS PRESIDENTIAL RECORDS over to the National Archives when he left office.... As REQUIRED under the LAW.
He didn't take any classified records with him, he took no presidential records with him, as Trump did.
So why in the world would the Archives ever need to ask Obama to return them?
Unlike Trump, Obama never took them with him when he left.
The archives had all of Obama Presidential records and the archivists when organizing the Obama records in preparation for FOIA REQUESTS and a president's library, they sort out classified records from non classified and separate them.
Once separated, the Archives held Obama classified records in a facility in D.C., and Obama non classified records in a facility in Chicago.