windows 10 – Will giving permissions and ownership to the administrator group also give permission to administrators on a different computer?

Say I set a file to have full control permission and ownership for the Administrators, if I transfer this to another computer with a different device name, will the file also have full control and ownership for administrators on that computer? If not, will changing the device name to the same as the original computer, make this the case? I ask because the administrator group has the device name before it, like this.