By default Notepad will save the text using ANSI encoding. This will use the default character set on the source computer and means that unless your other computer has the same character set you won't see the same results. The solution is to save your file in a universal encoding, either Unicode or UTF-8. These encodings map the Russian characters to the Unicode standard so are independent of any default character set on your, or anyone elses, computer.
From Notepad choose File->Save As... and pick Unicode or UTF-8.
Then when you open the file on any other computer it should display as intended.
Note: You only need to do this once for each new file. Since the file has now been marked as Unicode/UTF-8 (with a Byte Object Marker - BOM) Notepad and Notepad++ will recognize the BOM and keep the file in the same encoding.