The dictionaries I've checked all translate it as "to write" but my Mexican girlfriend assures me that this fails to capture the whole meaning. What's the closest word or phrase in English?
to draft or sometimes
to compose? It seems what I've gathered from definitions such as these is that it is a formal verb that covers all the actions involved in the professional composition of documents.
Redactar comes from the ver
to write in Spanish but is a word that joins the idea of writing something that has passed as: "Luis redacta todas las cartas en el periódico".
So I will still use write as part of your sentence and I will probably add up some words that it will intensify the meaning of it as:
Luis is the one in charge of writing and editing all the letters at the newspaper
As Diego suggested, compose and edit can help out to develop the meaning of your sentence.