I have purchased Turbotax 2022 Deluxe which I can access only through web login - can I convert this to Desktop version?

Do you have a full PC or Mac that meets the system requirements?   The CD/download cannot be used on any sort of mobile device.

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

Did you start 2022 in the Online version?  First save the tax file from Online. You can download the .tax2022 data file without paying for Online and continue in the desktop version
https://ttlc.intuit.com/community/saving/help/how-do-i-save-my-turbotax-online-return-as-a-tax-data-file/00/25740

You need to install the program on your computer and move your online return to the Desktop program. How to switch…….
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).