Stief Group is going to be the expert on this.

Purchase Orders for Adagio does update Transaction History in Adagio Inventory.

After doing the Dayend in Purchase Orders for Adagio, print the Audit List for the new receipt. When you start Adagio Inventory, you will see this message, ‘There are historical item transactions to retrieve. Do you wish to retrieve these transactions? Yes/No’. Select Yes.

I did a quick test and after following these steps, when I view the Transaction History for the item received, I do see the Receipt.