After transferring the Unlock Key/.auz file to your computer, open Live and choose the Load Unlock Key button in the Unlock dialog and locate the Unlock Key on your hard drive.Download and transfer the Unlock Key/.auz file to the computer that you have installed Live on.
Please get in touch with Ableton Support to receive the last supported version of Live. Note: You can find the instructions to authorize Live 10 and 11 here: In order to authorize version older than Live 10, follow the instructions below.
Authorizing older versions of Live (1 - 9.6.2)