In his book The End of Early Music..., performer-musicologist Bruce Haynes discusses transcribing recorded improvisations:
Some improvisers believe it is impossible to transcribe improvisations. But then, the best performers of written music give the illusion that they are improvising (since to read mechanically is the kiss of death). Besides, composing is often a matter of repeating a good invention often enough to be able to remember it and get it down on paper. The act of writing down the notes is actually a mechanical process that consists of documenting an idea that already exists. The creative moment has already taken place when the invention or inspiration occurred to the composer while performing or practicing. Often, of course, this will be followed by a structural organization that can sometimes be achieved only on paper (Haynes 2007, 209).
The structural organization of ideas on paper is indeed a way to codify ideas that already exist (as discussed in more detail in the subchapter Improvisation9 in the chapter On Scales of Improvisation) but these ideas can also be realized directly in performance, recorded, and organized on paper through the process of transcribing the recording.