Authentication Chaining/Proxy with Mutual Authentication

Hi folks. I'm a developer researching some customer requirements that involve our application working within the context of an F5 acting as a proxy between our application and our intended destination.

The application will be configured to talk to a URL for which the F5 terminates. The requirements are that we perform mutual authentication with the F5 thereafter, the connection is forwarded to the intended target where we must authenticate again; this time using basic authentication.

My question for the community is can the F5 store the credentials for this connection and simply perform the authentication on our behalf upon successful x509 authentication?

If yes, what feature-set does this correspond to in the F5 software/hardware suite and is this tied to a specific minimal firmware revision/hardware model?

Thanks in advance for your insight.