Setting your project to targeting AnyCPU should allow it to run on a 32-bit machine, provided that you are not using a library that loads 64-bit native code. If you have any dependencies, you should also use AnyCPU or 32-bit versions of these dependencies. Also, make sure that the standard .NET Framework is installed on the 32-bit machine (.NET 4.5 by default if you are using VS 2012 with a new project).
Please note that by default in VS 2012 for new projects there is AnyCPU, with the Prefer 32 Bit option. This will lead to the fact that it will always work as a 32-bit application, even on your 64-bit OS.
Please note that since your friend works with XP sp3, you cannot use .NET 4.5..NET 4.5 is not supported on Windows XP. You will need to change the application to the target .NET 4.0, which will then work on the XP computer (if it installs the 4.0 framework).
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