Finding the origination Purchase Order, via the posted vendor invoice.
It depends how you create the Posted Purchase Invoice, as there are multiple ways:
1. If you create the Posted Purchase Invoice directly from a Purchase Order by clicking Post and then Invoice or Receive and Invoice -> in the Vendor Ledger Entries the Description field will contain the Purchase Order Number:
If you Open the Posted Purchase Invoice itself you will be able to see the Purchase Order Number in there as well:
2. If you create the Posted Purchase Invoice from a Purchase Invoice by using the 'Get Receipt Lines...' function to invoice one or more Purchase Orders on one invoice -> the Purchase Order Number will not be available in the Vendor Ledger Entries, the reason for this is because as mentioned one Posted Purchase Invoice can contain multiple Purchase Orders.
In this case, if you open the Posted Purchase Invoice, the Invoice will also not display the Purchase Order as there can be more than one, but if you select a line item, if you click on Document Line Tracking you can see the Purchase Order the line item came from this way: