iOS - Office 365 Outlook for iOS (How To) Archive an Email Message
This document explains how to archive an email message.
Tap the message you would like to save, and then tap the Archive icon at the top of the screen. The Archive icon looks like a file folder with a downward facing arrow on it.
If you do not already have an Archive folder created, you will be prompted to either create an Archive folder or choose a specific folder to save the messages to.