Universal Directory? and MFA

Our customer has already set up Okta for their workforce. They have already told us they have set up MFA.
We want to use Okta for our application, and link their Okta to our Okta so that they can log in to an instance of our application with their users. I’ve been told this is possible, but I don’t know what it’s called (Universal Directory?)
Would the MFA details automatically be replicated across and they wouldn’t have to change anything? Would we be charged for each user (plus MFA costs) that were brokered across?

Does your application support federation (SAML or OAuth/OIDC)?

Not at the moment. It uses spring security with user and pass in USB but we’re going to change the spring configuration to use Okta as the auth server.