How can this be better expressed?
In respect of Anna's written wishes, there will be no funeral.
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There are several good ways to express the thought. Here are a few:
We will respect Anna's written wishes and forgo a funeral.
We will respect Anna's written wish to forgo a funeral.
As Anna requested in writing, there will be no funeral.
At Anna's written request there will be no funeral.
To respect Anna's wishes, no funeral will be held.
There will be no funeral per Anna's written request.