Well for a professional production the choreographer will likely have an assistant who helps them in the process as well as a dance captain(s) to assist in rehearsals. If the director and choreographer are not the same person, there is normally a lot of collaboration there as well.
Every choreographer has a different system of notation. Some write out every movement in detail including drawings of formations, blocking, etc. But that is different depending on the situation. Many modern dance choreographers use a format called "Labanotation" for converting movement into words on a page but I'm not sure if that is prominent among Broadway choreographers. Of course it is easier in this day and age because rehearsals and performances can be videotaped for preserving material.
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