I agree 100% with zxc. Although perfectly acceptable from a grammatical point of view, you'd be unlikely to hear this kind of sentence very often in practice. Except possibly in some kind of dispute where part of the sentence may be particularly stressed.
eg.maybe:
-it is an honour for us to have been invited
-Don't be silly! you don't mean that
-no,no, I insist . For us to have been invited is a huge honour.

Does it equalIs it equivalent to 'To have been invited to the party prompts in us an inordinate pride.' in meaning?
Yes, exactly, although there is also another type of for+to+infinitive clause which can't be so easily separated and which does fit well as the subject of the sentence

eg.
For 13 of our students to have been selected is a truly outstanding achievement.

For Boustany to have been found in breach of care by two Panels is pretty extraordinary under the circumstances.

Here the for + to is more like an infinitive-based that-clause. In fact it means pretty much the same thing as "that + should". ie. in the above sentences "For 13 of our students to have been selected..." and "For Boustany to have been found..." are close in meaning to "That 13 of our students should have been selected..." and "That Boustany should have been found...".