Can a user authenticated via claims be mapped to that user's Active Directory Account?

Question

I would like to provide a user that logs in through claims the same experience as if he or she logged in via his or her AD account. Have the same permissions, be a member of the same audiences, have the same tasks assigned, etc. I assume the only way that I can accomplish this is to map the claim to the AD account but I am open to other suggestions. How can I go about accomplishing this goal?