To give a user full mailbox rights, to be able to send meeting requests as another user do the following:
1. Open Migration Command Shell
2. Type: Add-MSOnlineMailPermission –Identity UserName1@DomainName -TrustedUser UserName2@DomainName -GrantFullAccess $True
Where username1 is the mailbox that you want to give Username2 permission to
3. Enter the proper admin credentials and make sure that the command shell replies with Successfully granted user account username1.domain.com full access permission to mailbox [email protected]