You want to know the last time a mobile device syncronized with Exchange Online.
Use the Get-MobileDeviceStatistics cmdlet.
There are many statistics, so you may need to select only the properties of interest.
Get-MobileDeviceStatistics -Mailbox <user@comp.any> |
Select-Object -Property DeviceID, DeviceType, DeviceModel, DeviceOS,LastSyncAttemptTime,LastSuccessSync, DeviceAccessState, DeviceAccessStateReason
Use this receipe if a user’s mail isn’t syncing to their mobile device.
I included the DeviceOS in the properties because a common issue with iOS devices is the need for re-authentication after an iOS update.