To move a mailbox to Exchange Online from Exchange 2013 first connect Windows PowerShell to Exchange Online with a Global Administrator:

$UserCredential = Get-Credential
$Session = New-PSSession -ConfigurationName Microsoft.Exchange -ConnectionUri https://outlook.office365.com/powershell-liveid/-Credential $UserCredential -Authentication Basic -AllowRedirection
Import-PSSession $Session
Provide the on-premise administrator credential

Then connect to the local Exchange 2013:

Run $RemoteCredential= Get-Credential
Start the move request

Finally initiate the move:

New-MoveRequest -Identity “useralias” -Remote -RemoteHostName “mail.mydomain.com” -TargetDeliveryDomain mydomain.mail.onmicrosoft.com -BadItemLimit 10000 -AcceptLargeDataLoss -RemoteCredential $RemoteCredential

source: http://www.e-apostolidis.gr/microsoft/exchange-2013-online-grand-full-access-to-mailboxes/