Magento2 Customer Save Event – How to Use

Follow this link for the event catalog_product_save_after to save your value. You can get your value in observer file and initiate your model object and save value in your table or use direct SQL queries to save in your table.

update your code with below code and try

<?php
namespace Vendor\Module\Observer;
use Magento\Framework\Event\Observer as EventObserver;
use Magento\Framework\Event\ObserverInterface;
class CustomereditPost implements ObserverInterface
{
protected $_request;
protected $_layout;
protected $_objectManager = null;
protected $_customerGroup;
private $logger;
protected $_customerRepositoryInterface;

/**
 * @param \Magento\Framework\ObjectManagerInterface $objectManager
 */
public function __construct(
    \Magento\Framework\View\Element\Context $context,
    \Magento\Framework\ObjectManagerInterface $objectManager,
    \Psr\Log\LoggerInterface $logger,
    \Magento\Customer\Api\CustomerRepositoryInterface $customerRepositoryInterface
){
    $this->_layout = $context->getLayout();
    $this->_request = $context->getRequest();
    $this->_objectManager = $objectManager;
    $this->logger = $logger;
    $this->_customerRepositoryInterface = $customerRepositoryInterface;
}

/**
 * @param \Magento\Framework\Event\Observer $observer
 * @return void
 */
public function execute(EventObserver $observer)
{
    $this->logger->info(' --jafar123--  ');
    $event = $observer->getEvent();
    $customer = $observer->getCustomerDataObject();
    $customerId = $customer->getId();
    $customer->getFirstName();
    $customerData = $this->_customerRepositoryInterface->getById($customerId);
    $customerData->setFirstName('jaf');
    $customerData->save();
    return $this;
}
}