QB Issue Resolution:

The export to desktop (US Only) provides you with a file that must be opened in desktop within 10 days, and the file has known problems, Some things do not export, inventory exports as service items with no history, payroll if you have it is exported as regular checks, these and other known problems have existed for over 9 years
see the limitations:
https://community.intuit.com/articles/1145409-export-limitations

Print out the QBO P&L, balance sheet, inventory valuation summary (if you have inventory), and sales tax liability as a minimum, compare the QBO reports to the same reports in desktop after you have a desktop company file – they must match, if not you have to find and correct the problems, intuit will not help

IMO if at all possible, it would be better to just re-enter all transactions in desktop

how to go from QBO to QBDT
https://community.intuit.com/articles/1145829-exporting-from-online-to-desktop

Resolution for Issue 'Convert from qbo to desktop' available: Yes (Solved).
Source: Intuit Community forum.

Convert from qbo to desktop: this issue or error code is a known issue in Quickbooks Online (QBO) and/or Quickbooks. Support for this issue is available either by self-service or paid support options. Experts are available to resolve your Quickbooks issue to ensure minimal downtime and continue running your business. First try to resolve the issue yourself by looking for a resolution described below. If it is a complex issue or you are unable to solve the issue, you may contact us by clicking here or by using other support options.

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