php - Is it possible to do a server redirect and simultaneously change the referrer to that of the redirecting domain?

I'd like to do a server redirect to another URL. Easy enough, for example in PHP:
header("Location: http://www.redirect.to.url.com/");
So a user visiting Site A clicks a link that goes to Site B that then redirects using the above server redirect to Site C.
The issue is that I'd like to change the referrer which gets sent on to Site C. Normal server redirect behavior is always to send the origin domain (Site A) in this case, and that is what site C receives. I'd like to change this so that Site C sees Site B as the referrer.
Can this be done?
Note that it has to be a SERVER redirect. I'm aware this can be done via on-page methods like meta refreshes and javascript. But those don't meet the server redirect criterion.
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