I am trying to finish my 2019 return that I started on-line. I have downloaded the program but it won't recognize the file downloaded from turbo tax online.

You have to download the tax data file from the online edition.  Then open the data file using the installed software.  Click on the File menu at the top left of the desktop program screen.  Click on Open Tax Return.  Browse to where you downloaded the tax data file.

To access your current or prior year online tax returns sign onto the TurboTax website with the User ID you used to create the account - https://myturbotax.intuit.com/

Scroll down to the bottom of the screen and on the section Your tax returns & documents click on Show.  Click on the Year and Click on Download .tax file

Did you download the file ending in .tax2019 from Online?  And installed the Desktop program ok?  Where are you getting stuck?  What happens when you go to File-Open and try to open the .tax2019 file?

To continue in the desktop version see this…….

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

After you get the program installed the first thing to do before you open your tax return .tax file is to update the program and install any state programs you had. Then open your file. So you first might need to start a fake return to be able to download the state program (go to FILE - NEW).