Steps to enable online archive in office 365 mailbox and move the data

a) Using Exchange Admin Center (EAC)

First, sign in to your Office 365 profile and click on app launcher icon and, then choose Admin.

Go to Admin centers from the bottom navigation of Office 365 admin center, and select Exchange option

exchange

Under Exchange Admin Center, you can select the Recipients and then, choose Mailboxes. Then, choose a required mailbox that you wish to archive and choose enable option under In-Place Archive

archive-choose-mailboxes

Note: Additionally, you can perform bulk archives to select multiple mailboxes. You can use Shift + Ctrl key together in order to select all mailboxes. After this, click on More options from the details panel. Then, choose Enable option under Archive.