Can you convert QuickBooks Online (QBO) version to QuickBooks desktop (QBDT) version?

You can, but it comes all kinds of hurdles. It is not recommended at this time.

If you have to, please read these two articles.

If you read the following instructions, it’s clear they have not made new improvements in this area for few years now.

      Detailed instructions ………… Note: You must log in as the QuickBooks Administrator to convert your company file and you must be using Internet Explorer to access QuickBooks Online.

      Lists & Transactions ……….vi Change the Browser Mode to IE8 Compatibility View.