php redirect / WordPress

The customer had an old non-wordpress site which had a folder called rsvp which did a redirect to a page in the old site.

In the new WordPress site, the equivalent location is this: http://rain1.com/new-site/customer-support/confirm-appointment/

So in the folder rsvp  on the server I put this index.php

<?php
// redirect to new Rain1 WordPress site RSVP page
header("Location: www.rain1.com/new-site/customer-support/confirm-appointment/");
exit;
?>

There is an htaccess page that (purposely) has this:

ErrorDocument 404 http://www.rain1.com/new-site

If I go to rain1.com/rsvp, I get the new site main page, NOT the desired page.

Why?

What is the correct way to do this?

Thanks