The donors referred to their campaign contributions as baked goods, usually “baklava.” They called Hillary Clinton “Our Sister” or “the Big Lady.”

And they referred to their ultimate sponsor by the initials H.H., for His Highness, Crown Prince Mohammed bin Zayed of the United Arab Emirates, one of the Pentagon’s closest partners in the Middle East and one of the biggest foreign spenders on influence in Washington.

“Will send you a note on the matter as per HH instruction,” George Nader, a trusted emissary for the crown prince, wrote in a text message in late June 2016, describing a million-dollar payment of “baklava,” according to an indictment unsealed by the Justice Department this week.

“I am leaving early morning back to join HH,” Mr. Nader wrote in another message a few months later to Ahmad Khawaja, a California businessman who was charged with acting as a conduit for Mr. Nader’s illegal contributions. “Have already told him about the Wonderful Event with Our Sister and he was thrilled and want to know all about it in person.”