Objective
Allow a non-global Office 365 administrator to replace profile pictures for other individuals in an organization.
Background
In a SharePoint on-premises farm, the SharePoint User Profile Service Management area can be secured to allow a non-farm administrator to administer an organization’s SharePoint user profile pictures. This is possible in an on-premises farm because a farm administrator has access to the site permissions of the Central Administration site collection where the User Profile are managed.
In SharePoint Online, the story is different. A similar security configuration cannot be set up because a global administrator does not have access to apply a similar security configuration. In SharePoint Online, the user profile administration pages reside in the administration site of the Office 365 tenant -- a place designated only for global administrators.
And if the requirement is to have user profile pictures extend across the Office 365 products including SharePoint Online, Skype for Business, Delve, etc., then the user profile pictures need to be managed from the Exchange Online Admin Center rather than from SharePoint Online.
Configuration
The Exchange Online Admin Center used for managing user profile pictures can be access via this generic link: https://outlook.office365.com/ecp/
To allow a designated non-global administrator user to manage profile pictures for others in the organization, the user must be given at minimum the "User Option" administrative role in Exchange Online.
This can be done as follows:
Set up a new role administrative role called "O365 User Profile Management," assign the "User Options" role and then assign the designated user.
Usage - Updating another user's profile picture
The designated user can now visit the Exchange Admin Center and use the "Another user…" option in their profile options to administer another account's Office 365 profile.
https://outlook.office365.com/ecp/
Select the target user then click "Edit information" to access the Office 365 user profile. Note that the interface shows a bar indicating that a user "is working on behalf" of another user.
Use the "change" photo button to update the user's Office 365 profile picture.
Final Step - Have target users visit Delve
Delve plays an critical role in propagating profile pictures from Exchange Online to the SharePoint Online user profiles. When a user visits Delve, that visit triggers the execution of a process that creates 3 versions of a user's profile picture within SharePoint.
As a result, in order to complete the update of a user profile picture across the Office 365 platform by a designated "profile picture administrator," the end user(s) will still need to be involved and visit the Delve page.
Oh, and in the event that you don't have an Office 365 subscription that includes Delve, you'll need to provide the users a link like the following (replacing YOUR-TENANT with the appropriate value) :