I suppose from your message, that you use WordPress multisite, and “mother instance” is a main blog, but “child instances” are subsites.
You should network activate User Role Editor.
Then after configuring ‘test’ role and ‘test’ user at the main blog, you may go to the “Network Admin->Users->User Role Editor” and click “Update Network” to replicate ‘test’ role to all subsites of this WordPress multisite installation.
Go to “Network Admin->Users”, select ‘test’ user and click ‘Capabilities’ link under his row. Then click “Update Network” button. This will add ‘test’ user with his current permissions (e.g. ‘test’ role assigned) to all subsites.