I started my 2020 return with the online Premier version. I purchased the desktop version. How can I transfer the data from online to desktop versions?

You need to switch to the desktop software to get what you paid for.  You have to download it, update it and open it up from your own hard drive to use it.  

https://ttlc.intuit.com/community/choosing-a-product/help/how-do-i-switch-from-turbotax-online-to-the-turbotax-software/00/26129

The online version won't let me save the partially completed return to a .tax2020 file.  I think this is because I didn't pay for the online version yet.  I want to do what-if analysis and save multiple files.  So I subsequently paid for the desktop version and I have installed it, but the Import menu does not provide an option from the Online version.   So I am still looking for a way to transfer the data I already entered into the online version to my desktop version.  

To call TurboTax customer support

https://ttlc.intuit.com/questions/1899263-what-is-the-turbotax-phone-number

Customer support is available from 5 a.m. to 9 p.m. Pacific time