On a Saturday afternoon last July, the day after John Kelly agreed to become President Trump’s chief of staff, an email arrived in his inbox. “Congratulations!” it began. “(I think!)”

The sender was Philippe Reines, Hillary Clinton’s longtime aide and image buffer since her time in the Senate. Reines met Kelly while working for Clinton at the State Department, when Kelly was a senior military aide to Leon Panetta, then the defense secretary. The two stayed in touch. After Kelly left military service in 2016, he joined the advisory board at Reines’s consulting firm, Beacon Global Strategies, cashing a couple of checks before he was summoned to Trump Tower.

“Can’t say I’m rooting for your boss, but I’m absolutely rooting for you,” Reines wrote to Kelly. “Especially if it takes the edges off him.” He offered some unsolicited advice: Stay off television. Tend to the mystique. Let the Kellyanne Conways and Anthony Scaramuccis talk up the president on cable. “You don’t want to be in that basket,” Reines said.