Contacts should sync from the web version to the downloaded version. Especially contact groups.
I like to use the downloaded version of Outlook for email on my laptop, but I cant use the contact groups is have set up on my previous computer or on the web version. These should sync seamlessly over all versions of the program wherever you are signed in...what's the point of a web based email if you have to change those things on each device you sign in on?
Souvonik Mondal - Outlook commented
My complete Outlook app for Android got messed up. My Outlook account in Android got screwed. Contacts from Outlook server is not syncing.