Samuel Lusker McCroskey (1893-1960) was a Brigadier General in the U.S. Army. Nabokov is most probably referring here to McCroskey's appointment in 1945 as Commandant of the Biarritz American University, when he occupied the Royal Suite of the Hotel du Palais.
Opened in summer 1945 by the US War Department as a post-war morale booster, to provide a university education to US military personnel awaiting redeployment or a return to civilian life, the university had 4000 places and took over the entire town of Biarritz. The town's casino was converted to the university library, and accommodation for 'students' was found in 40 luxurious hotels and nearly 100 villas where the rich of Europe had previously come to spend winters. Teachers were academics brought over from American universities and colleges as well as actors or artists, including singer Marlene Dietrich who taught drama.
Another American university - also up and running within 60 days of V E Day - was set up in Europe, in Shrivenham, UK as the SAU (Shrivenham American University). The British Army's Military College of Science now occupies the old SAU premises.
Both universities were closed in March 1946, having provided a short education for approximately 18 000 American soldiers. A street sign in Biarritz, "Rue de l' Université Americaine, 1945-1946" still bears witness to the educational experiment.
After retiring from the army, McCroskey joined Douglas Aircraft where he worked on the development of the Nike and Hercules missiles.