Index: src/wp-includes/class-phpmailer.php
===================================================================
--- src/wp-includes/class-phpmailer.php	(revision 48034)
+++ src/wp-includes/class-phpmailer.php	(working copy)
@@ -6,6 +6,9 @@
 if ( function_exists( '_deprecated_file' ) ) {
 	_deprecated_file( basename( __FILE__ ), '5.5.0', WPINC . '/PHPMailer/PHPMailer.php', __( 'The PHPMailer class has been moved to wp-includes/PHPMailer subdirectory and now uses the PHPMailer\PHPMailer namespace.' ) );
 }
+
 require __DIR__ . '/PHPMailer/PHPMailer.php';
+require __DIR__ . '/PHPMailer/Exception.php';
 
 class_alias( PHPMailer\PHPMailer\PHPMailer::class, 'PHPMailer' );
+class_alias( PHPMailer\PHPMailer\Exception::class, 'phpmailerException' );
Index: src/wp-includes/class-smtp.php
===================================================================
--- src/wp-includes/class-smtp.php	(revision 48034)
+++ src/wp-includes/class-smtp.php	(working copy)
@@ -4,4 +4,7 @@
  * The SMTP class has been moved to the wp-includes/PHPMailer subdirectory and now uses the PHPMailer\PHPMailer namespace.
  */
 _deprecated_file( basename( __FILE__ ), '5.5.0', WPINC . '/PHPMailer/SMTP.php', __( 'The SMTP class has been moved to the wp-includes/PHPMailer subdirectory and now uses the PHPMailer\PHPMailer namespace.' ) );
+
 require __DIR__ . '/PHPMailer/SMTP.php';
+
+class_alias( PHPMailer\PHPMailer\SMTP::class, 'SMTP' );