Forum Discussion
Online Archive on Outlook app (iOS)
I don't think the Online archive is available in Outlook for iOS and Android. It's been requested in UseVoice on this https://outlook.uservoice.com/forums/293349-outlook-for-ios/suggestions/16609312-exchange-online-archive-accessfor example to no avail.
The Online archive is available in the abandoned but I still assume supported https://itunes.apple.com/gb/app/owa-for-iphone/id659503543?mt=8. This is a holdover from the Acompli acquisition and not going back to add this feature. I guess it isn't seen as being very important or there is some technical limitation that makes this difficult to implement.
I suppose if Microsoft ever retires the OWA app, they will add support but who knows. It would be great to get an official steer.
No ActiveSync-based client (including Outlook for iOS) supports access to an archive mailbox because the protocol has not been updated to accommodate this resource (same reason as for shared mailbox). The OWA mobile app is essentially a wrapper around the browser version running on a mobile client, so it has access to all resources. However, that client has not been in active development since the Acompli (Outlook for iOS and Android) acquisition in November 2014 and limps on in a state of limbo.