Ahhh...yes, that is a different proposition.
It *could* be done, but it would take a moderately complex bunch of PHP code to do so.
Yes, PHP can "spoof" cookies and can post data on your behalf, but then you still have other problems to contend with. Such as spoofing the HTTP_REFERER. And more, depending on how strong the protection is on the site you are trying to spoof.
Needless to say, what you are trying to do is what most sites (especially Google, by the by) are doing their best to prevent.
An optimist sees the glass as half full.
A pessimist sees the glass as half empty.
A realist drinks it no matter how much there is.