Jan,
so the Product Owner is the "Scrum Product Owner" of the customer, and the Project Manager is some kind of "Scrum Product Owner" of the company.
When comparing to Scrum, the ASAP "scrum team" will consist of Development Team, Scrum Master and Project Manager. And the Product Owner is the external product owner of the customer.
Project Manager (company) and Product Owner (customer) work together to get the requirements fixed. However, only the Project Manager is allowed to maintain the product backlog of the development team, right?
Hopefully I don't mix up things here.
Regards
Tobias