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I believe - after having searched for the proper translation a little more - that "Erstkopie" should be the proper translation. I also found "Nullkopie" - a term that is allegedly equivalent to "Erstkopie" at least according to one webpage. Other webpages suggest "answer print" for "Nullkopie". So, I'll go with "Erstkopie".
Thanks to you, Tobi, and thanks to everyone who took the time to respond! I appreciated your input! 4 KudoZ points were awarded for this answer
Explanation: Not sure if this is the best translation. Print = Kopie. First-run presumably refers to theaters that show (only) recent releases. I'm not sure that this concept of a first-run theater even exists in Germany.
ntext United States Local time: 17:03 Native speaker of: English, German PRO pts in pair: 1878
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