You want to display only if message user is given user role or who is seeing that user is given user role?
Which role you want to display?

Please let me know the role slug of those users (“business users” role slug) who have business listing.

Please add following code in your theme’s (child theme’s if any) functions.php

add_action( 'fep_display_after_message', function(){
	$authordata = get_userdata( get_the_author_meta('ID') );
	
	if( in_array( 'administrator', $authordata->roles ) ){
		echo '<a href="' . esc_url( home_url( 'business-directory/' ) ). get_the_author_meta('user_nicename') . '">' . get_the_author_meta('display_name') . '</a>';
	}
});

Change ‘administrator’ to whatever your user role is. For testing purpose i have used ‘administrator’ so that you can check that only ‘administrator’ role users link will show.