Let me answer your imported concern directly to guide you accordingly, @RodenA. 

Invoices and deposits should import into your QuickBooks Desktop (QBDT) transparently. I'll share a few reasons why some transactions are not been imported to QBDT). So it will be correct at the earliest opportunity.

Here are the possible reasons why your transaction won't convert in QBDT: 

1. The rounding differences in the two versions can cause failed export of payments to specific invoices. If this is the case, correct the amount of the invoice and request payment.
2. Ensure that you didn't use multicurrency to keep your data exported correctly. 
3. QBDT should be in the latest release to avoid any issues. 

Also, to know how the transactions converted to QBDT, see the following details below: 

• Invoices that contain charges, credits, billable expenses, or time associated with sub-customers will separate into one invoice per customer.
• If a refund is from a bank, refund receipts convert to Credit memos and checks.
• If the refund is from a different account, it will convert to a general journal entry.
• Bills, checks, credit card charges, credit card credits, vendor credits, journal entries, and deposits
• Transactions with numerous Accounts Receivable or Accounts Payable line converts to multiple journal entries. 

For more details, see this link: Limitations when you convert from QuickBooks Online to QuickBooks Desktop. Directly go to the Transactions section. 

To ensure that your books match and that the information is imported correctly, I suggest running Profit and Loss on QuickBooks Online. Then, compare it to the same report in QBDT on an accrual basis. For more information, see Step 5 in this article: Export and convert your QuickBooks Online data to QuickBooks Desktop.

If the issue continues, I'd recommend contacting our Customer Care Team. They may investigate your account to know why invoices and deposits are not imported into your account. Follow the steps outlined by Candice in this thread. Make sure to reach them within business hours to ensure a swift response.

In addition, see this article on how to import lists in QBDT: Move lists and balances from QuickBooks Online to QBDT. 

If you still have questions in mind, please let me know by leaving a comment below. I'm always here to help you again. Keep safe, RodenA.