sessionStorage saves input value in browser but it is not loaded in the form field

You are using innerHTML for every field.

Input field shouldn’t be using .innerHTML use .value instead and for select you should loop through the options not use .innerHTML

window.onload = function() {
    var quote_price_input = sessionStorage.getItem("quote_price_input");
    var message_to_customer = sessionStorage.getItem("message_to_customer");
    var select_price_option = sessionStorage.getItem("select_price_option");

    if(quote_price_input !== null) {
    document.getElementById('quote_price_input').value = quote_price_input;
      } else
    document.getElementById('quote_price_input').value = "";

    if(select_price_option !== null) {
        var sel = document.getElementById('select_price_option');
        var opts = sel.options;
        for (var opt, j = 0; opt = opts[j]; j++) {
            console.log(opt.innerHTML);
            if (opt.innerHTML == select_price_option) {
              sel.selectedIndex = j;
              break;
            }
        }
      }

    if(message_to_customer !== null) {
    document.getElementById('message_to_customer').innerHTML = message_to_customer;
      } else
    document.getElementById('message_to_customer').innerHTML = "";
};

// Before refreshing the page, save the form data to sessionStorage
window.onbeforeunload = function() {
    var quote_price_input = document.getElementById('quote_price_input');
    var message_to_customer = document.getElementById('message_to_customer');
    var select_price_option = document.getElementById('select_price_option');

    if(quote_price_input !== null) {
        sessionStorage.setItem('quote_price_input', $('#quote_price_input').val());
    }

    if(select_price_option !== null) {
        sessionStorage.setItem('select_price_option', $('#select_price_option').val());
    }

    if(message_to_customer !== null) {
        sessionStorage.setItem('message_to_customer', $('#message_to_customer').val());
    }
}