When A. R. Alexander left the US in 1945 one of his trainees, Dolly Dailey, took over the training course and ran it until 1949. (It is not clear whether this course was condoned by A. R. Alexander.)
Lulie Westfeldt trained some teachers in the late 1940s (from which Judith Leibowitz qualified in 1949).  (Alma Frank writes in a letter in 1947: ‘Evidently Lulie is training teachers already.’)
After Alexander’s death in 1955 his training course was continued by Margaret Goldie, Walter Carrington, Irene Stewart and John Skinner, first at Ashley Place and from April 1956 at Bainbridge Street in London. In 1960 Walter Carrington moved to 18 Lansdowne Road, London W11, and the training course became the Constructive Teaching Centre.
Patrick Macdonald moved into Ashley Place in April 1956 and started a training course shortly afterwards.
Marjory Barlow and Wilfred Barlow ran a training course 1950–52, and restarted it shortly after Alexander’s death in 1955.
Marjorie Barstow started a three-year training course around 1972, but discontinued it as she switched to an apprenticeship style of teaching.
Judith Leibowitz trained teachers at the American Center for the Alexander Technique (ACAT) in New York from 1964–81.
Peter Scott ran a teacher training course 1972–78.
Post-1975 a number of other teacher training courses started. ‘The School of Alexander Studies’ run by Paul Collins and Elizabeth Collins (also Rajna, later Langford), was the first ‘second generation’ STAT-approved training course (starting around 1975).
For a ‘family tree’ draft of all (known) Alexander Technique teacher training courses since 1931 please see this 5-page PDF (1.6 MB). Including F. M. Alexander there have been at least 133 teachers training courses in total.