The owner account with Intuit is Gmail.  And, yes, all user accounts and all Intuit products are under the owner's Gmail. This includes FAM and QuickBooks, and QuickBooks online (some of our clients use this and we are the accountants associated with those client QBOL accounts).

Although all users are under the owner's Gmail, we each use our personal email address for login credentials for all Intuit products, with some of us using Gmail and another using sbcglobal.  Because we're a small firm, we all have Admin access to all areas. 

Another piece to the puzzle, in case is has any bearing on this: while I've been talking to the person to whom this case was escalated late 2020, he asked why we have more than one realm.  I was unable to answer that because I'm unaware of what realms are.  We have one account with Intuit for ProSeries, QB desktop and QBOL.  However, when I log into ProSeries or Link, I'm offered two different "realms." One seems to be associated with only our QBOL clients and the other is everything else Intuit. I may have noticed another one at one point, but I'm not remembering.  It might have been Link, but I'm not sure.

Thank you for confirming that Gmail is not the culprit here.  I agree and since that first support encounter after we made the switch to Gmail, no support person has ever tried to tell me this.

I can confirm that this happens with both old and new clients. That was one of the things that Support asked me to try back in November/December. All clients that were invited yesterday were invited through ProSeries.

Here is another complexity: after yesterday's invite, I logged in to Link with the owner's credentials and saw only some of the clients to whom invites were sent.  This morning we received a notice that one of the clients had started completing their virtual organizer.  The name does not show up on the Clients page, but when I click under "Client activity" on the far right of the page, I can view what this client has answered and sent so far.  

Again, thank you for your time addressing this and trying to resolve it.