Hi Madalin,
In ECS you may not see any PO output message in ECC as PO is just copied there.
As you said that you don't receive any idocs from their system the only possible option is to use PI to send the PO output in the form of XML message. In SRM, there is a possibility to enable the supplier (within BP) for XML output.
In SRM 7.0, PI will hold the supplier web address (URL) to send this XML output to. It is called method call in SRM where XML message is generated as PO output.
Please visit my other posts for detailed config.
Regards,
Ravi Pachauri