Hi there, @hhbookkeeper.
Let me add some ideas on how to resolve billable expenses that cannot match with the actual invoices.
Since there's no report that shows purchases and its invoices, make sure to identify the invoices created in Shopkeep. You can check the amounts, discounts, and marked up price of each item created in the invoices.
You can pull up a transaction report that allows you to view register transaction data from Shopkeep. It will serve as your remedy on how to create those invoices in QBO and able to match it with the billable expenses.
If the billable expenses not matched with the proper customer, it will lose track of the associated transactions like invoices.
I've added a video on how to enter billable expenses and associate it with invoices in QuickBooks: Enter billable expenses.
Also, I recommend consulting your accountant for accounting advice in interpreting and matching the billable expenses with the corresponding invoices.
Feel free to post a comment below if you need further assistance. I'm always here to help. Stay safe and well!