Greetings Admiral.
Open Windows Command Prompt (press Windows + R and type:
%HOMEPATH%\AppData\LocalLow\Game Labs\Ultimate Admiral Dreadnoughts
press enter afterwards
A folder will appear, there are two files:
Saved designs are saved in "mission_data.xml"
Mission progress (and game settings) are saved in "settings.xml"
However, transfer of these .xml files on a different PC is not supported, you can try to copy/paste the files but there is a risk to cause problems. If his game is not running after that, you can delete these files and they will be re-generated once you launch the game again.