Updating address book outlook
Group membership-based address lists and global address lists rely on Member Of attribute filtering.
This step could be done on one of your ADFS farm servers that has Windows Azure Active Directory Power Shell (WAAD Posh) installed.
There is a variety of ways to perform this assignment.
The one provided here is by no means the only one or the most elegant one, but it works. You have to have Exchange Online and Office 365 connections in the same WAAD Power Shell session for the next step.
This next post is going to talk in detail about GAL segmentation setup in Office 365.
The original idea was borrowed from this Microsoft blog post, but since not all of the steps were covered there in sufficient detail, I am expanding them here, and adding two specific examples: how to segment GAL based on distribution lists membership, and how to segment GAL based on Office attribute.