My German often suffers from "The umlaut is silent"

What exactly should that mean?

As a native German I can tell you that o and ö are not the same letter.
And they are pronounced differently. So I don't understand your "silent".

(e.g in Groebner/Grobner).

Well, if you write/say Flote or Krote instead of Flöte (flute) or Kröte (toad), then a German would probably either understand that you have problems with umlauts of (if the German does not have an understanding for other languages) even look at you and hardly understand you at all.

People write Floete or Kroete on keyboards that do not have the umlaut letters on them and this is usually commonly understood.

Ralf

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