One of the companies, Concord Management and Consulting, has fought the special counsel’s charges in court, demanding that the government demonstrate it willfully violated the law. Friday’s criminal complaint, with its detailed descriptions of the conspiracy continuing for months after February’s indictment, appears to do just that.

Image An image provided by the Justice Department shows a social media post used in the influence campaign.

Earlier Russian influence campaigns stood out for their clumsiness — Facebook posts from the Internet Research Agency, another arm of Project Lakhta that conducted Russia’s social media disruption campaign in 2016, often contained broken English and off-topic cultural references.

But the new operations appear to have been more sophisticated, with smoother messaging and a better command of American political discourse that allowed for more precisely targeted campaigns. Operatives instructed their colleagues to frame posts about former Senator John McCain, Republican of Arizona, who tangled frequently with Mr. Trump before he died in August, as an “anti-Trump geezer.” Speaker Paul D. Ryan, they said, should be described as “an absolute nobody.”

Operatives were instructed to attack Republicans who failed to sufficiently champion the construction of the border wall that Mr. Trump has sought; to stress the need for strict voter identification laws, especially in “blue states”; and to highlight “scandals that took place when Mueller headed the F.B.I.” in an attempt to discredit the special counsel’s investigation.

Acknowledging the time difference between Russia and the United States, one conspirator advised the others to post in the morning to attract liberal audiences during the American evening — “L.G.B.T. groups are often active at night,” the operative wrote — and to seek out conservatives awake in the morning by posting just before they left work for the day.

They also developed strategies for blending in to partisan American audiences. “If you write posts in a liberal group … you must not use Breitbart titles,” read one message sent to the Russian group, referring to the conservative American news site. “On the contrary, if you write posts in a conservative group, do not use Washington Post or BuzzFeed’s titles.”

The group also gave suggestions, some of them racist, for reaching specific affinity groups. One member suggested keeping posts simple when they were aimed at lesbian, gay, bisexual and transgender groups of color, writing that “colored L.G.B.T. are less sophisticated than white; therefore, complicated phrases and messages do not work.”