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We have "demo/demo" user in "registered" usergroup. After login he can see "JS Notifications" module.
But also we have "Anatoli81" user in the same "registered" usergroup and with the same settings. But he can't see "JS Notifications" module (I also can't see it in source code).
"JS Notifications" module has Public Access.
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it seems your site has server cache, i changed module position and back it to notification position, still, after clear Joomla cache, i can see the module in the sidebar.
Also, I need the database access of site to check the user permission.