Um, okay, if that's what you want to do.
Open a socket connection to the second page, make the POST, then redirect the browser to the second page. The browser will request the second page without any data, but that's okay, because you just made a request that did have it.
Needless to say, there's no inherent reason why the two pages have to be the same.
But why do you want to do this, anyway? Why not just submit to print.php, which, before doing its own thing, opens a socket connection to register.php and POSTs? Both pages will do their thing in the right order, and the browser will end up on the right page.