Try to find the installation file. It should be an executable (.exe) exstension like "install.exe". That should work.
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You can copy it but it works only for simpler applications like Firefox, MSN messenger and so on. But Adobe Photoshop checks for registry files and if the program fails to locate those files in the computer registry then your program may fail to start up. External Hardrives work the same way as USB flash drives do when connected to another computer. You can try to "cheat" the program but I dont know how you will do that.
and if it is a single user license, you willl only be able to use it on one computer and on any other computers.
Whatever you try to do beyond this is "unethical".

Does that answer you question?
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The first question is what operating system are you using?

If you are using a MAC OS-X computer it is easy, just move the folder containing the program and associated files to the new drive and open the program from there. There should be no other complications.

If you are using Windows the process, if possible at all, is much more complicated because Windows installs programs differently. During the installation process Windows may install the executable in one location and certain libraries and enabling files (DLLs, CABs ) in another location. Windows also makes entries in a special file called the Registry to tie all these things together. (I am not a Windows expert and realize that my explanation is probably faulty or simplified in some regards)
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