Please follow this procedure to change the signature to a specific user:
Click on Users' details in the Users & Set-up and scroll way down
Here can you see currently assigned signature template and if it's inherited from a Group or not.
Click on Change assignments.
Cancel inheriting by unticking the checkbox Inherited from Group.
You can now choose which of your templates will be assigned specifically to this user.
The users that don't inherit the signature template from their group can be recognized in the User group menu by the broken chain link indicator:
To reverse the process, follow the above mentioned procedure and make sure you tick the checkbox Inherited from Group.
This option also works for marketing templates and company profiles.