function fake_sticky_posts_for_author() {
    $user = wp_get_current_user();

    if ( get_current_user_id() && in_array('author', $user->roles) ) {
        return get_posts( array(
            'author' => get_current_user_id(),
            'fields' => 'ids',
            'posts_per_page' => -1
        ) );
    }

    return false;
}
add_filter( 'pre_option_sticky_posts', 'fake_sticky_posts_for_author' );
// we use pre_option_sticky_posts in here, since we want to ignore value of this option, so there is no point to load it