Often times, we will get an issue, where we need to check if any issues have occurred due to a move request but the move request (and seemingly any information related to it) has been removed.
Luckily, we also write/log this information for later retrieval. We can obtain the log and place it in a text file on the desktop (assuming the '~' signifies the default home directory in PowerShell) via the following method:
((Get-MailboxStatistics <user alias OR smtp> -IncludeMoveHistory -IncludeMoveReport).MoveHistory).Report | Out-File C:\Users\johnbai\Desktop\report.tx
The report will need some clean-up, for readability-sake. I have attached a sample from my O365 tenant for reference.