I got help with solving a problem in this thead: Redirect with POST data. Now that I decided that the whole site and even this function must work when JS is disabled I need
Use CURL extension to post request to payment server when processing your user's request on server-side.
If your user must be redirected to some external web site, than save needed data first and then redirect him using header()
function. Keep in mind that in this case you wouldn't be able to use POST method for making request to remote payment server.