Need a word for having rewritten something after translation

I have written a book.

Well, actually, my mother-in-law told the story of her experiences as a German forced laborer in the Soviet Union after World War 2. This was given in German and recorded onto audio tape a number of years ago by my sister-in-law. My S.I.L. later transcribed the story in German onto twenty or so tightly typewritten foolscap sheets, and a few years ago she gave us a copy of this. My wife and I eventually translated this into very rough English (we both speak German, my wife being a native speaker). It is quite a story and we have determined to self-publish it as a book. So this is what I need: a word (or two) for having put it into a final form for the book.

See, the original telling was done pretty much as it occurred to her to tell it, and it tends to get lost in parts, backtrack, go forward, and around the bend at times. The final version is still her story, but it has been reworked into what I hope is a readable and understandable whole, with a beginning, a middle and an end. I've also a spot of research on historical matters pertaining to the story, and because some words she used were Russian, I used Google Translate and the Russian Language SE to get some more information.

On the title page, I am giving the title of the book, followed by the subtitle, then the author attribution: by Gertrud Baltutt.

Below the author attribution (she is now deceased, btw), I want to indicate that the work is a transcription and a translation of the original tale, and the word I need is for the really hard part, putting it into a coherent form for publication. Here's what I got, so far:

by Gertrud Baltutt

As told to her daughter Cyberherbalist's Sister-in-Law.
Translated by
her daughter Mrs. Cyberherbalist
and XXXXXXed by Cyberherbalist

What is that word (or words)? Arranged? Edited? What?

A secondary question is this: my mother-in-law did not actually write this book. It's her story, but when it comes down to it, I wrote it, or at least co-authored it. I tried to maintain the flavor of the original German, but is it really her who is the author? Or me? With her being deceased, there's not danger she'll get upset with me about it, so whatever.