I’d like to ask that-clause is an adverb clause of the verb or complement of the object in the sentence?
*****
NOT A TEACHER *****
Great question.
I have made up this sentence: "We write to inform
you that Harvard University has accepted your application."
If I understand my books correctly:
"you" is an indirect object.
"that Oxford University has accepted your application" is a
noun clause serving as the
direct object of the infinitive "to inform."
*****
I have found this sentence in a book that is greatly respected:
"May I inform
you that your order is ready for collection?"
Here is a very important statement: "With some verbs, ... it is impossible to delete the [indirect object]."
Only my comment: It is NOT acceptable to say "May I inform that your order is ready for collection?"
But the book says this sentence is fine without "me": "The professor
showed (me) that Pythagoras was right."
-- Quirk, Greenbaum, Leech, and Svartvik,
A Comprehensive Grammar of the English Language (1985 edition), page 1212.