Past conditional agreement with past participle of être. (été) e.g. she would have been happy..

Question

Accepted Answer

Hi Clare,
You don't say where you got that sentence from.
She would have been happy = Elle aurait été heureuse 
I'm not sure if you are querying whether the past participle of être - été agrees. If so, the answer is no; it is invariable.
Hope this helps!

Answer

What, in particular, is your question and in reference to which lession is it?

Answer

Clare,

2 grammar rules that are in play to answer your question ( and extend it to all compound forms of être ) :

1. ‘ aurait été ‘ - compound verb form of être, which conjugates with avoir, and would have past participle agreement if the direct object preceded the verb

Special cases when the past participle agrees (in number & gender) when used with 'avoir' in the compound past in French (Le Passé Composé)

however

2. être is intransitive and never has a direct object so the past participle in all compound verb forms of ‘ être ‘ is always ‘ été ‘

https://www.larousse.fr/dictionnaires/francais/%C3%AAtre/31549

Special cases when the past participle agrees (in number & gender) when used with 'avoir' in the compound past in French (Le Passé Composé)