I'd like to post an answer that also uses curl to get the contents, and mpdf to save the results to a pdf, so you get all the steps of a tipical use case. It's only raw code (so to be adapted to your needs), but it works.
// import mpdf somewhere
require_once dirname(__FILE__) . '/mpdf/vendor/autoload.php';
// get mpdf instance
$mpdf = new \Mpdf\Mpdf();
// src php file
$mysrcfile = 'http://www.somesite.com/somedir/mysrcfile.php';
// where we want to save the pdf
$mydestination = 'http://www.somesite.com/somedir/mypdffile.pdf';
// encode $_POST data to json
$json = json_encode($_POST);
// init curl > pass the url of the php file we want to pass
// data to and then print out to pdf
$ch = curl_init($mysrcfile);
// tell not to echo the results
curl_setopt ($ch, CURLOPT_RETURNTRANSFER, 1 );
// set the proper headers
curl_setopt($ch, CURLOPT_HTTPHEADER, [ 'Content-Type: application/json', 'Content-Length: ' . strlen($json) ]);
// pass the json data to $mysrcfile
curl_setopt($ch, CURLOPT_POSTFIELDS, $json);
// exec curl and save results
$html = curl_exec($ch);
curl_close($ch);
// parse html and then save to a pdf file
$mpdf->WriteHTML($html);
$this->mpdf->Output($mydestination, \Mpdf\Output\Destination::FILE);
In $mysrcfile I'll read json data like this (as stated on previous answers):
$data = json_decode(file_get_contents('php://input'));
// (then process it and build the page source)