Migrating your business applications, such as Exchange Server, to the cloud can reduce maintenance costs, improve availability and deliver cost savings.
Note that you’ll have to wait up to 24 hours to get audit data. Click Search & Investigation -> Click Audit log search -> Click Start recording user and admin activity.You have to be an Office 365 Admin to enable auditing.
How to Enable Mailbox Audit Logging and Review Audit Logs in Office 365.