Hello TanyaM1,
I have confirmed this is possible and when you rang desktop we think they have miss understood what you were saying therefore told you, you cannot do this. I have reached out to our desktop team and they have confirmed there is no direct migration from one to the other, but like stated in previous posts you can export your data out of quickbooks online and into desktop and told you which ones you can do as below.
In your Quickbooks Online, you can export by CSV files for your customers, suppliers, products and services and chart of accounts out and into your Quickbooks Desktop product.
To export customer, suppliers out of quickbooks online is if you go to the cog wheel>under tools>export data>lists>toggle on suppliers and customer>export data out. this will move the data out and on to an excel spreadsheet.
to export chart of accounts out of online, if you go to accounting>chart of accounts>run report top right hand corner> 3rd icon in next to printer and cog wheel is a page that is export>click drop down arrow on that icon and export to excel.
Any transactions you need to take out i would csv the files again out of the online product and ask your accountant if they can put them into your desktop as they have the function to do that but normal user doesn't.
