Moving management account to another organization

Hi, we have set up AWS SSO to our billing/management account with several other accounts as members of this AWS organization. We now need to move our accounts to a service provider who manages our billing instead. Will our SSO still works in this new set up?

Do we need to set up AWS SSO for each accounts that will belong to another billing accounts? Also will we lose capabilities to centralize our policies from a management account which we now control? Thanks