Hi Marcel,
which integration are you using, Ariba P2P with SAP ERP as system of record, or Ariba Network integration?
For a GR Confirmation notice to flow back from ERP to Ariba, message cXML Receipt Request needs to be implemented.
You can find guidance for implementin either integration, P2P or network, using respective rapid-deployment solutions. You can find and download them here: for P2P at http://service.sap.com/public/rds-aribap2p and for network integration http://service.sap.com/public/rds-ariba
Cheers,
Andreas