Germans cooked King Edward, presenting fish-eater with bill (9)

I believe the answer is:

merganser

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'fish-eater with bill' is the definition.
I can't judge whether this defines the answer.

'germans cooked king edward' is the wordplay.
'cooked' indicates an anagram (letters cooked into a new form).
'king edward' becomes 'er' (abbreviation for Eduardus Rex).
'germans' with letters rearranged gives 'mergans'.
'mergans'+'er'='MERGANSER'

'presenting' acts as a link.

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(Other definitions for merganser that I've seen before include "Diving duck" , "Diving bird" , "Diver" , "Sawbill" , "Together saw bill" .)

I've seen this clue in The Independent.

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