By moving users from Lync on-premises to the cloud, we will lose some of the parameters. The operation requires the Lync administrative tools and the PowerShell module for Lync Online to be installed on the same computer. If we install the module for Lync Online before the administrative tools for Lync 2013 Server, the OCSCore.msi file overwrites the LyncOnlineConnector.ps1 file, and New-CsOnlineSession will require a -TargetServer parameter. In this situation, we have to reinstall the Lync Online module (see the following post on the Microsoft support site at http://support.microsoft.com/kb/2955287).
Remember that to move the user to Lync Online, they must be enabled for both Lync Server on-premises and Lync Online (so we have to assign the user a license for Lync Online by using the Office 365 portal). Users with no assigned licenses will show the error Move-CsUser : HostedMigration fault: Error=(507), Description=(User must has an assigned license...