Remember form field values with page navigation

Use sessions

<?php
session_start();

 // your fomrfields
$post_fields = array( 'key_one', 'key_two', 'key_three' );

$form_data = array();

// copy needed form data from $_POST array
foreach ( $post_fields as $key )
  if ( isset( $_POST[$key] )
    $form_data[$key] = $_POST[$key];

// save your form data in a session if no form data was saved before
if (
  ! empty( $form_data )
    &&
  ! isset( $_SESSION['form_data'] )
)
  $_SESSION['form_data'] = serialize( $form_data );

// read saved form data from session
if (
  isset( $_SESSION['form_data'] )
    &&
  ! empty( $_SESSION['form_data'] )
    &&
  empty( $form_data )
)
  $form_data = unserialize( $_SESSION['form_data'] );

From now on use $form_data[key] instead of $_POST[key]