Which api allow me as developer to move a video into a folder?
I, for example, have the video https://vimeo.com/12345678.
In my personal area, I created the folder "DEV" under "Video". Opening in the browser, it is linked as https://vimeo.com/manage/folders/20417534
I tried the following call
POST https://api.vimeo.com/me/albums/20417534/videos/12345678
But I got an error complaining about album doesn't exist.
I supposed this is not the right API to call.
Which API must I call to specify in which folder to save the video?
You're using the /me/albums/ path, which is incorrect. You need to use the /projects/ path instead (Vimeo originally named the feature "projects" but later changed it to "folders". The API still uses the original naming convention).
To add the video at /videos/12345678 to the folder at https://vimeo.com/manage/folders/20417534, make this request:
PUT https://api.vimeo.com/me/projects/20417534/videos/12345678
Alternatively, you could replace the /me/ path with /users/666666666/ if you want to use your userid, but /me/ is a nice shortcut, since this request can only really succeed with your own folder anyway.
That endpoint is documented here: https://developer.vimeo.com/api/reference/projects#add_video_to_project