How to Link Purchase Order Invoices back to Project Costs?

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Hi All 

We're working on a Project Statement report that brings back a comprehensive breakdown of the project costs and revenue. For the costs, we were able to bring back Payables invoices pretty easily as they are joined via the original header/distribution/line IDs. However, we are finding it extremely difficult to bring back invoices relating to Purchase Receipts (Oracle Fusion Cost Management). I uncovered the Parent Distribution ID from Projects (pjc_exp_items_all.parent_dist_id) which does seem to link to POs but we are getting varied results (I have tried linking to the po_distribution_id from ap_invoice_distributions_all through a left outer join peia.parent_dist_id = aida.po_distribution_id (+).