JSFiddle - React, Tailwind, and code Playground

HTML

<div class="grid-container case-page-image">
  <div class="grid utility-model">Пример utility-model 1</div>
  <div class="grid industrial-design">Пример industrial-design 2</div>
  <div class="grid copyright">Пример copyright 3</div>
  <div class="grid industrial-design">Пример industrial-design 4</div>
  <div class="grid invention">Пример invention 5</div>
  <div class="grid copyright">Пример copyright 6</div>
  <div class="grid utility-model">Пример utility-model 7</div>
  <div class="grid industrial-design">Пример industrial-design 8</div>
  <div class="grid invention">Пример invention 9</div>
  <div class="grid copyright">Пример copyright 10</div>
</div>

JavaScript

//получаем  последние 4 diva в контейнере
$arr = $('.grid-container div');
let foDiv = [...$arr.slice(-4, $arr.length)].map(item => item.outerHTML).join(' ');

//сохраняем в localStorage
localStorage.setItem('foDiv', foDiv);

//на след странице вытаскиваем с localStorage html
localStorage.getItem('foDiv');