These files that you are referring to will be downloaded to a temporary folder of which it's location will be different depending on several things particularly your operating system.
Even on the same computer if you do the installation twice, the files will likely be downloaded to different locations.
Some common temp locations wherewhich the Garena LoL installer may use for installationsthese files are:
- C:\Windows\Temp
- C:\Users\ComputerName\AppData\Local\Temp
- C:\Temp
- C:\tmp
In order to find the files that the installer downloads you can use a program called Search Everything.
Once installed click on the Date Modified tab in order to sort every file on your computer, so that the most recently created/modified files are shown on top. Note: the first time you click "Date Modified" will take a considerable amount of time, you can see that it's working by the Sorting... in the bottom left.
Once you've sorted it in this way, begin installation and the files that the installer creates/downloads will be shown near the top of this list. Once you identify the files you are interested in just look at the Path tab, or you can right click on the file and select Open Path which will open the folder that that file is in.