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The correct answers to the above solution-question is by else programming basic:

if( current_user_can('administrator')) { 
<!-- only administrator will see this message -->
        }
else { 
        if( current_user_can('author')) {
} else {
<!-- only author but no administrator will see this message -->
?>
<style type="text/css">#perhapsDIVremovalidentifier{
display:none;
</style>
}
<?php
}
}

Brief: The administrator is found, but if we push author the administrator is as well found. So we just let administrator pass through and identify the author only.