1. He has been awarded a prize for his work on ...

2. He was to have been awarded a prize for his work on ...

In the second sentence, what I want to say is this man refused to accept the award though it was announced officially.

My question is the words 'have been'. I know they are correct.

However, the word 'he' should combine with 'has been'.
I find this odd. Your comments, please.
In #2 the operative verb is was, in concord with the subject he. To have been is the infinitive perfective of be, here used in a passive construction. (To be to + infinitive is a modal idiom and we have it here in the past tense.)
The past tense (OK, perfect) form of the infinitive:
to be -> to have been
In passive:
to be awarded -> to have been awarded

Also, search with
perfect infinitive
(top right Search box)
and you'll find many good threads.
Site Hint: Check out our list of pronunciation videos.
Thanks Micawber for the reply.

What is the meaning of infinitive perfective?

Be is the verb here.

The infinitive 'to be' behaves as follows:

I am/was ...

You are/were ...

He/She is/was ...

They are/were ...
 Marius Hancu's reply was promoted to an answer.
Students: Are you brave enough to let our tutors analyse your pronunciation?