Re-enable use of Admin SID in Magento after SUPEE-11314

After SUPEE-11314 or upgrade to Magento 1.9.4.5 use of Admin SIDs is disabled by default, which may affect certain modules (i.e. Sage Pay Suite MOTO payments).
To re-enable use of Admin SIDs we can add corresponding section into backend:

--- app/code/core/Mage/Core/etc/system.xml
+++ app/code/core/Mage/Core/etc/system.xml
@@ -1610,6 +1610,16 @@
                             <show_in_website>1</show_in_website>
                             <show_in_store>0</show_in_store>
                         </use_frontend_sid>
+                        <use_admin_sid translate="label comment">
+                            <label>Use SID on Admin Backend</label>
+                            <comment>Allows admins to stay logged in via SID</comment>
+                            <frontend_type>select</frontend_type>
+                            <source_model>adminhtml/system_config_source_yesno</source_model>
+                            <sort_order>60</sort_order>
+                            <show_in_default>1</show_in_default>
+                            <show_in_website>0</show_in_website>
+                            <show_in_store>0</show_in_store>
+                        </use_admin_sid>
                     </fields>
                 </session>
                 <browser_capabilities translate="label">

After that we Flush Magento cache, navigate to System > Configuration > Web > Session Validation Settings and change value of Use SID on Admin Backend option to Yes. Please do not forget to Flush Magento cache to apply changes.