This may simply be a headache of trying to work between 2 different was of handling mail. Gmail uses labels, not really folders. Outlook uses folders. I occasionally use Outlook for my Gmail account at home when I want to do some different searching than I do directly in Gmail. I've noticed that the labels in Gmail show up as folders in Outlook, but as far as Gmail is concerned, they are just labels.

Things I'd want to try:

1. Create a label in Gmail web app, sync things up, see if it translates to the PC where they tried to create the folder. If it does, maybe easiest fix (if this is easy) would be to apply a label in Gmail to all emails that would be included - hopefully it's searchable, such as "From:bob@someemailaddress.com" Then let that sync into Outlook on the different machines.
2. In case it is a PC issue, not really a conflict between different tools, I'd want to try a different user profile on Windows, connect Outlook via that profile and see if the desired outcome can be handled there. If that works, then they may need this: 1. Export the one problematic folder to a PST file, 2. Create new user profile to replace current user profile (just rename the old/damaged one initially, so you can easily pull whatever files necessary for new profile. 3. Also, as part of that, there are some registry keys it's best to delete rather than just renaming the user profile folder.
3. A hail mary shot if it seems to just be the computer would also be to run sfc /scannow and then chkdsk /f /r from administrative command line or powershell window, and see if that gives any luck. If it's a whole PC thing, as crazy as it sounds, this might correct it.

My gut tells me it's more #1 in the list above than anything, but tossed out a couple of other seemingly odd ideas that occasionally fix really make-no-sense issues.

"But thanks be to God, which giveth us the victory through our Lord Jesus Christ." 1 Corinthians 15:57

Okay - good points. I'll analyze what is the easiest to try first.

So, I opened a ticket with Microsoft and they said to "export the folder to a PST and then re-import into your mailbox" - more or less. I exported the folder, no problem. Then I tried to DELETE the problem folder from my list of folders and it would not allow me to delete it. So, this to me is the problem. It's a zombie folder and thus did not sync to the Gmail server and of course wouldn't sync to other computers. I created a NEW folder and opened the exported PST file and I could drag the email into the new folder. Then it synced to Gmail as seen in Gmail Web Mail interface.

How can you not be able to delete a folder? I even tried Outlook safe mode to see if I could delete the folder. And I said that I had previously done a SCANPST of the entire .OST file.

Any idea why this folder is on crack?

My only guess at this point (sorry so slow - rarely check in here anymore) goes back to Google vs Microsoft email structures. Google uses labels, Microsoft uses folders. They aren't really the same thing, but they kind of make it work between the two.

If it were possible, I'd want to delete the label in Gmail (somehow keep a list or an exported backup of the items, if want kept). Then in Outlook, make sure it's totally disconnected from the account. Maybe export to a new PST, don't connect the PST to any account, try to delete the folder in new PST.... IF it works there (and I'm not saying it will), try to connect that PST to the Gmail account.

That's definitely an odd one with modern email.

"But thanks be to God, which giveth us the victory through our Lord Jesus Christ." 1 Corinthians 15:57

The "folder" doesn't exist in Gmail so I cannot delete it there. The folder cannot be deleted in Outlook. I wonder if it could have something to do with the user creating the folder on his iphone in IOS email? I don't KNOW that he did that, but that would add another variable. Weird. The real issue is whether he has any other "problem folders" that he doesn't even know about.

I'm not dealing with any PST files here EXCEPT for exporting the contents of the problem folder which I then re-imported immediately and deleted the PST.