salaam alaikum brothers and sisters,
i was in a lecture today and the lecturer talked about an incident.
he said, during yazid(la)'s caliphate, abdullah ibn umar went to yazid(la) and told him that the way he was abusing ahlulbayt

because they didnt give bay'ah or allegiance to him was wrong and haraam. Yazid (la) then went and took out a letter and give it to Abdullah ibn umar and told him that this is the letter your father umar gave to my father muawiyah(la). In that letter, umar had described amongst other thing, what the plan was to force bay'ah from ahlulbayt

to Abu bakr and what happened that night.
Apparently in that letter, umar describes what the plan was on how to force ahlulbayt

to give allegiance to Abu bakr and also describes what happened when they carried out the plan, including the abuse he(umar) gave to lady Fatima(AS), as in how he burnt down the door and pushed it onto her.
IS this true? did umar right a letter to muawiyah (la) describing all this stuff. any references?
Your help will be appreciated jazkallah.
wa-salaam