A member of the Cuban national team and two-time Most Valuable Player, he had several .300 seasons, and holds the distinction of being the only catcher ever to have caught a no-hitter in Caribbean Series history.

[3] Prior to his professional career in Cuba, Fleitas was a member of the Cuban National team that won two Amateur World Series in 1939 and 1942, earning MVP honors in the latter victory, after batting a top average of .405.

[6] The Cuban Lázaro Salazar, manager of the Industriales de Monterrey, spoke to Pasquel about Fleitas, who was offered a $20,000 contract plus $200 for monthly expenses.

[8] While the significant increase in salary allowed him to purchase a home in Santa Fe,[7] his stay in Mexico effectively nixed any chance he would have playing in the majors.

In response to Pasquel actions, MLB Commissioner Happy Chandler banned all players for five years that left the United States for the Mexican League that did not return before his deadline.

Only when former New York Giants outfielder Danny Gardella threatened to sue the Major League Baseball hierarchy, did the owners relent and lift the ban.

[3] He replaced Guerra as the team's primary catcher during the 1945-46 campaign and batted .313 with a second-best 32 RBI, three behind league and MVP Alejandro Crespo.

The next day, reliable left-handed Agapito Mayor won a complete-game pitching duel against Fred Martin and the Leones by a score of 2–1, being highlighted by Fleitas, who tripled the winning run in the 7th inning to obtain the narrow victory.

At the end, Fleitas won MVP honors, beating out established big leaguers like Bobby Ávila, Alex Carrasquel, Sandy Consuegra, George Hausmann, Red Hayworth, Lou Klein, Minnie Miñoso, and the aforementioned Gardella and Lanier, among others.

[3] He was greatly improved in the 1949-50 season, going 81 for 262 for a .309 average in a career-best 68 games, helping his team win a second consecutive title and a trip to the 1950 Series, where he batted 5 for 25 with two runs and three RBI for a disappointing Almendares that finished in third place.

He responded with a batting average of .304 (7 for 23), including a double, one RBI and two runs, helping Habana win the Series with a 5–0 record, and also was selected for the All-Star team.

In addition, Fleitas became the first man to catch a no-hitter in Series history, when he caught Tommy Fine in his 1–0 gem against the Cervecería Caracas of Venezuela in Game 2.