Hello Alli and welcome to Wefugees.
We are happy to help you and thank you for your question. I have done a little research.
The fingerprints that are taken from you in Luxembourg can only be taken under suspicion of criminal offences by the German state from the EURODAC. If you apply for asylum in Germany you will be fingerprinted again.
On an official site of the German state the following was said about this:
The primary purpose of storing the fingerprint is not to protect the document against forgery. Rather, in case of doubt about the identity of the person identifying himself and the person depicted on the photograph of the document, it should also be possible to establish identity directly. This would also eliminate the need for time-consuming inquiries to other authorities, which are currently still necessary in cases of doubt. enable the person concerned to continue his or her journey quickly or to take advantage of the freedom of movement
(BMI 2022: Wozu dient die Aufnahme von Fingerabdrücken? letzter Zugriff: 15.11.22)
The page is unfortunately only in German. https://***.bmi.bund.de/SharedDocs/faqs/DE/themen/moderne-verwaltung/ausweise/eu-verordnung-erhoehung-der-sicherheit/4-fingerabdruck.html;jsessionid=860CBEB674B64B421BF63F0821BD4B09.2_cid295
I will link our experts @meike and @mbeon-éanna here, they **** over my answer again and complete it. We wish you all the best! Feel free to come back to us if you have any further questions.
With best regards Saskia