I may change this if you add additional information, which changes the scenario significantly.
If you really lock down a directory on an external drive so only one account can read it (usually externals allow everyone full access by default), let's say even a common account like administrator, and then you move it to another computer, even the administrator on the new computer will not be able to read it. The reason is that even though they have the same username, they have different SSID's (security identifiers), so are actually different in the eyes of the OS.
You may find that pass-through authentication may allow the new administrator to see it, that is, if they both have the same username and password. Of course, on a network, if you are talking a domain administrator, even if you gave it the permissions locally, that is the same user and SSID on another domain computer. Lastly, there is no real security, since if you plug that into any Windows computer, any administrator can take ownership of all the files, and then give himself any permissions they want.