Compare fields in CiviRule?
Yes you can do some comparison in CiviRules using the Field Value Comparison condition. Assuming that your external ID is a custom field (in CiviCRM an external identifier has to be unique....) you might be able to work your way through. It might mean you have to develop a specific condition though.
And please note that the &quot;link them together as a partner organization&quot; is an action, not a condition :-) And it will definitely be bespoke development, but possible.