Did Mozart composed alphabet song?

In the 1780s, Mozart made the tune of it. (originally for the song he composed, "Twinkle Twinkle Little Star") But then 50 years later an American music publisher, Charles Bradlee, put the ABCs to that tune and copyrighted it in 1835. Mozart made the tune of the Alphabet song, (and Twinkle Twinkle and Baa Baa Black Sheep) not the lyrics.