Ted Healy was not considered one of the Stooges.
Moe, Larry, and Shemp started off with Ted as ‘Ted Healy and his Stooges’. Shemp left after two (?) films with MGM, and Curly replaced him. Eventually, due to many disputes between MGM and the 4 of them, their contract expired and Columbia offered just the boys a deal in 1933. ‘Woman Haters’, their first short, was a musical number which was highly acclaimed and loved throughout the country. Eventually, their third short for Columbia, ‘Men in Black’, was nomianted for an Oscar and the boys' career skyrocketed. Curly had a stroke on the set of his final short with the Moe and Larry, and had to leave due to it. Eventually Shemp came back, and the rest is history.