In the fall of 2017, an administrator at George Mason University’s law school circulated a confidential memo about a prospective hire.

Just months earlier, Neil M. Gorsuch, a federal appeals court judge from Colorado, had won confirmation to the Supreme Court seat left vacant by the death of Antonin Scalia, the conservative icon for whom the school was named. For President Donald J. Trump, bringing Judge Gorsuch to Washington was the first step toward fulfilling a campaign promise to cement the high court unassailably on the right. For the leaders of the law school, bringing the new justice to teach at Scalia Law was a way to advance their own parallel ambition.

“Establishing and building a strong relationship with Justice Gorsuch during his first full term on the bench could be a game-changing opportunity for Scalia Law, as it looks to accelerate its already meteoric rise to the top rank of law schools in the United States,” read the memo, contained in one of thousands of internal university emails obtained by The New York Times.