Okay, I've got it figured out.

There are a few things that need to be changed.

Open:
/editors/fckeditor/editor/filemanager/connectors/php/config.php

Find (on line 33 and 34):

// Path to user files relative to the document root.
$Config['UserFilesPath'] = '/myfiles/' ;

Change it to:

// Path to user files relative to the document root.
$Config['UserFilesPath'] = '/images/' ;


Also find (near the bottom)

$Config['DeniedExtensions']['File'] = array() ;
$Config['FileTypesPath']['File'] = $Config['UserFilesPath'] . 'file/' ;
$Config['FileTypesAbsolutePath']['File']= ($Config['UserFilesAbsolutePath'] == '') ? '' : $Config['UserFilesAbsolutePath'].'file/' ;
$Config['QuickUploadPath']['File'] = $Config['UserFilesPath'] ;
$Config['QuickUploadAbsolutePath']['File']= $Config['UserFilesAbsolutePath'] ;

Change it to:

$Config['DeniedExtensions']['File'] = array() ;
$Config['FileTypesPath']['File'] = $Config['UserFilesPath'] . '/' ;
$Config['FileTypesAbsolutePath']['File']= ($Config['UserFilesAbsolutePath'] == '') ? '' : $Config['UserFilesAbsolutePath'].'/' ;
$Config['QuickUploadPath']['File'] = $Config['UserFilesPath'] ;
$Config['QuickUploadAbsolutePath']['File']= $Config['UserFilesAbsolutePath'] ;



I've tested these settings, and they work.