The department had argued that the memo was exempt from public records laws because it consisted of private advice from lawyers whom Mr. Barr had relied on to make the call on prosecuting Mr. Trump. But Judge Jackson, who was appointed by President Barack Obama in 2011, ruled that the memo contained strategic advice, and that Mr. Barr and his aides already understood what his decision would be. “The fact that he would not be prosecuted was a given,” Judge Jackson wrote of Mr. Trump. She also singled out Mr. Barr for how he had spun the investigation’s findings in a letter summarizing the 448-page report before it was released, which allowed Mr. Trump to claim he had been exonerated. “The attorney general’s characterization of what he’d hardly had time to skim, much less study closely, prompted an immediate reaction, as politicians and pundits took to their microphones and Twitter feeds to decry what they feared was an attempt to hide the ball,” Judge Jackson wrote.