Afaik that information is only partialy available in the vCenter Task and Events log.
See also the Task and Events tab in the vSphere Client.
You can get the timestamp, the user and the destination, but the other info is not present
Get-VIEvent -MaxSamples 500 | where {$_.GetType().Name -eq "TaskEvent" -and $_.Info.Name -eq "MoveIntoFolder_Task"} | select CreatedTime,UserName,@{N="Destination";E={$_.Info.EntityName}}
You can change the MaxSamples value if you want to go back further in time.