Share data between authenticator and IdP authenticator

I have an url that a have a parameter(legacy_id) and I am trying to get it in a custom a Authenticator and store somewhere to recover it in a IdP authenticator.
The url also have the kc_idp_hint to redirect to the IdP.

Keycloak Version 21.1.0

Context:

The Authenticator where I am trying to store de legacy_id is within the browser flow but the IdP authenticator is in a different flow only used by Identity Providers.
I have tried to store in a AuthNote or UserSessionNote but they are not share between flows.

Is it prossible to that?

Thank you.