After adding a new user into Office 365, the user has to be allowed to read/write some shared calendars within the organization.

First of all you will need to connect to Office 365

Add permission to the Calendar

Add-MailboxFolderPermission\Calendar -User -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\Calendar -User

To remove permissions for a specific user:

Remove-MailboxFolderPermission -Identity calendar@company:\calendar -user