Try below event Magento 2 :-

<event name="customer_save_after_data_object">
    <observer name="customer_save_after_observer" instance="Vendor\Sales\Observer\CustomereditPost" />
</event>

Magento 1 : -

<config>
    <adminhtml>
        <events>
            <adminhtml_customer_save_after>
                <observers>
                    <My_WebService_customer_register_success>
                        <type>singleton</type>
                        <class>My_WebService_Model_Observer</class>
                        <method>customerRegisterSuccess</method>
                    </My_WebService_customer_register_success>
                </observers>
            </adminhtml_customer_save_after>
        </events>
    </adminhtml>
</config>

Try below event

Magento 2 :-

<event name="customer_save_after_data_object">
    <observer name="customer_save_after_observer" instance="Vendor\Sales\Observer\CustomereditPost" />
</event>

Magento 1 : -

<config>
    <adminhtml>
        <events>
            <adminhtml_customer_save_after>
                <observers>
                    <My_WebService_customer_register_success>
                        <type>singleton</type>
                        <class>My_WebService_Model_Observer</class>
                        <method>customerRegisterSuccess</method>
                    </My_WebService_customer_register_success>
                </observers>
            </adminhtml_customer_save_after>
        </events>
    </adminhtml>
</config>

Try below event

<event name="customer_save_after_data_object">
    <observer name="customer_save_after_observer" instance="Vendor\Sales\Observer\CustomereditPost" />
</event>

Try below event Magento 2 :-

<event name="customer_save_after_data_object">
    <observer name="customer_save_after_observer" instance="Vendor\Sales\Observer\CustomereditPost" />
</event>

Magento 1 : -

<config>
    <adminhtml>
        <events>
            <adminhtml_customer_save_after>
                <observers>
                    <My_WebService_customer_register_success>
                        <type>singleton</type>
                        <class>My_WebService_Model_Observer</class>
                        <method>customerRegisterSuccess</method>
                    </My_WebService_customer_register_success>
                </observers>
            </adminhtml_customer_save_after>
        </events>
    </adminhtml>
</config>