You shouldn't use the "last" ("L") directive in the RewriteRule! This will prevent all further rewrite rules to be skipped whenever a Basic or Digest Auth is given, which is almost certainly not what you want.
So the following lines are sufficient for the .htaccess (or httpd.conf) file:
RewriteEngine On
RewriteRule .* - [E=HTTP_AUTHORIZATION:%{HTTP:Authorization}]
