Dependency between closed Project and AP Invoice matching.

We need some clarification on the dependency between closed Project and AP invoice matching. The situation is like this:

1. PO has been created and received for a Project, when the Project was open. Then Project was closed.

2. Now we are facing the issue, that we cannot match invoice to this PO, cause the Project was closed.

3. Despite of the fact, that PO has been already received.

To process the invoice do we need to temporarily open project. If so why ?

Thanks,

Siva