Hey Detlef,
You should not need to copy the same file in the frontend. All you need is the joomla API
In your componentname.php file in the frontend you could do (example from hotspots):
$jlang = JFactory::getLanguage();
$jlang->load('com_hotspots', JPATH_ADMINISTRATOR, 'en-GB', true);
$jlang->load('com_hotspots', JPATH_ADMINISTRATOR, $jlang->getDefault(), true);
$jlang->load('com_hotspots', JPATH_ADMINISTRATOR, null, true);
first line loads the admin English file. (this ensures that all strings will have a meaningful translation and not COM_HOTSPOTS_MY_AWESOME_SOMETHING_TEXT...)
the second line loads the language of the site (which can be German for example) And the third line loads the user language. (it can be for example Japanese).
With those 3 lines you can use the same admin language file in the frontend and you don't need to copy files around. 1 location = less things to maintain and less thinks can brake.
Cheers,
Daniel
edit: With this approach you can do even merging. For example you can grab the frontend language file and add it to the backend. Or you can load the files of a module or plugin in your component. Whatever you need...