If your computer is Windows, this will not be possible. Just by downloading the same installer you will achieve this.
Whether it's Linux or OS X, you can copy the folder where Studio is installed. Because in this case the android does not actually "install", it just moves the files to the program directory and creates a shortcut.
On Linux, Android Studio is usually installed by default inside the / opt folder. Now in OSx go to the finder, find the AndroidStudio shortcut, double-click on it and select "Show contents of the Package" copy the contents folder.
But nothing will get better if the other machine does not have java installed or is from different operating systems.
Good luck!