we can get the frontend quote of any order using the quote api repository and the quote id.
\Magento\Quote\Api\CartRepositoryInterface $quoteRepository, in construct function.
$quote = $this->quoteRepository->get($order->getQuoteId()); But this will not help full in getting the admin quote. We have to use only the admin session there to get the quote. The sample code snippets are written here(http://webhintsexplorer.com/magento-2-admin-recreate-cart/ ). It will be very helpful.