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it can be joomla cache problem. please try to clear the cache first. and after that you can invite any users to private group. after invited user accept the invitation, you will have that email at mail queue. let see this issue still happen or not.
if still, i need your FTP access detail for debugging purpose.
FYI: put any credential information at site info form, by editing your first post at this topic.
Thanks, did seem to get quite a few of these to start with but seemed to have stopped now and doing the test you suggested worked ok. Will mark this as closed now and start new ticket if it happens again.