That’s not what the information on the websites for Bundesgesundheitsministerium and the airports read. It says that if you have a negative test result from your departure country, in either German or English language, and the time of the test is not more than 48 h before entry, you do NOT have to undergo the mandatory test within 72 h and do NOT need to quarantine. It does not, however, state if you need to submit such test result to the authorities or if it’s sufficient to check the appropriate box on the landing card that you had one taken no more than 48 h ago.

You are correct though that you need to have the test result handy in case the authorities want to verify the correctness of your statement. Based on what I read and heard on the German news, the mandatory tests are not being enforced upon entry and are done based on the honor system. That’s why you don’t need to do the test at the airport upon arrival and can go to your primary care physician instead within 3 days after arrival. If you don’t, you’re subject to a hefty fine.

I’m a dual US/German citizen and am flying to Germany for a visit tomorrow. Just had the COVID test done today and the result came a few hours later. I have no intention of taking another test in FRA based on the information provided by the authorities. Nothing suggests that you need to have both done or submit anything to the Gesundheitsamt. It even states that a negative test result won’t be reported to the authorities even when the test is taken in Germany. So if they don’t do it, why should I?