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@company.com:\Calendar -User dude@company.com -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@company.com:\Calendar -User dude@company.com
To remove permissions for a specific user:
Remove-MailboxFolderPermission -Identity calendar@company:\calendar -user dude@company.com