Hello,
I have SMTP POSTFIX on my server and users are connecting there over outlook from windows. I would like to receive every mail that is sent from specific mail adress to the internet. Is that possible?

Thanks

Not sure if there's a possibility, but I'd certainly hope there's none.
What with invasion of privacy on a large scale etc...

there is no privacy invasion - the server is in a company.. and only bussiness matters should be handled there..

See here.

Beware that this method is not safe. It merely injects a BCC: address which can still expose what is going on to the sender (rejections that would bounce for any reason will bounce even for a BCC).

Ideally, genuine audit trail logging and such should use a reliable pure file storage mechanism (that verifies complete write to hardware and possibly a backup completion, too). That is, when mail enters the system to the point it will be considered for processing (even if that is just to check if it is spam and reject it), it should be stored into a system file, perhaps not unlike a Maildir. Unfortunately, Postfix does not implement any such mechanism. When I proposed this idea over a decade ago, the reaction I got suggests that people who work heavily with email can only think of this in terms of delivering email, rather than simply storing it in a file