Sadly, vCenter is still not super awesome about logging, but vROps does show this under the Summary|Parent Folder metric. You should be able to create an alert in vROps that fires when the value is not whatever you set.
Thank for your reply. I won't be able to use that vROps setting because we have hundreds of folders and subfolders. I need some way simply to alert us if a VM changes folders... bonus if the alert named what folder was the source and what was the destination, along with a username of who made the change. I'm going to dig around further in vLI and perhaps the logs of vCenter itself. If anyone has other ideas... please chime in, thank you.
One thought I had was that we *could* export the env every day with PowerShell and then find some programmatic way to compare files the next day to see if anything has changed and what... kind of like nMap for VMware folders. This seems like a huge uplift though.
The problem here is not with vRLI but that there is nothing that is pushed into a log on vCenter's side with that information. Even when using the vRLI agent with a proper agent group (which grabs all the various vCenter services logs), this isn't written much less sent. I tested this in my 6.5 environment, so maybe in 6.7 it's there. Your request is a good idea, so I hope you submit it as a feature request if you determine it's still not present in 6.7.