After adding a new user into Office 365, the user has to be allowed to read/write some shared calendars within the organization.
Add-MailboxFolderPermission email@example.com:\Calendar -User firstname.lastname@example.org -AccessRights Author
Note: AccessRights can be: Owner, PublishingEditor, Editor, PublishingAuthor, Author, NonEditingAuthor, Reviewer, Contributor, AvailabilityOnly, LimitedDetails
Get permission for a specific users
Get-MailboxFolderPermission -Identity email@example.com:\Calendar -User firstname.lastname@example.org
To remove permissions for a specific user:
Remove-MailboxFolderPermission -Identity calendar@company:\calendar -user email@example.com