Agile is more of a brand then a methodology, which type do you mean in particular?
In scrum for example, yes, it would be common to map a previous project manager to a product owner. Although much of the responsibility of the project managing would fall to the scrum master and the team, the skill set required to be a PO (communicating the customers needs, managing customer expectations, directing team efforts towards business value and being the guy who's accountable) are close to those of a PM. However, it is also possible to have a more technical PO or one that more directly represents the customer.
Here's the thing though. The fact you have product management team to conflict suggests that that text above isn't really relevant, because you may be doing cargo cult agile, with the PM and the PO replicating each others work. Do you still have a traditional project manager for example?