How Can I transfer my download program of TurboTax to a different computer

See the help article How do I move my tax data file to another computer?

Since you now have to log into an Intuit Account when you first install it, all your downloads and licenses are listed there (even if you bought it from somewhere else) so if you need to install it again or install on another computer, even on the other operating system (Windows, Mac) you can download it again.  See screen shot.

Then you can open your tax return file you copied from the old computer.   After you get the program installed or reinstalled the first thing to do before you open your tax return 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). Enter some basic information, then go to the state tab and download the state program. Then try to open your existing return, go to FILE - OPEN