Perhaps a special 'contact' type form (like Contact Form 7) that is restricted to the specific user. They could fill out the 'message' area of the form, send it, and the back-end of the form would send it to your subscriber list.
Or the form could send it to you for approval, if needed. Note that this process is just a one-time thing; no storage of the content other than sending. (Although there are some CF7 add-ins that would allow saving of the content into a database.)
Added 26 Nov 2017: Check into the Email Subscriber and Newsletters plugin. It allows you maintain a subscriber list, and send out newsletters with a 'rich text editor' type interface. You can also set it up to send out a canned notice whenever a new post is published. I've just used for the 'new post' notifications, along with the occasional (one-time blast) newsletter. Good plugin, with good support.