Transfer Store from one Multi-Store Install to Another Multi-Store Install

We have 2 clients; each with multiple stores, one for each of their child companies. Client B bought a company from Client A, so we need to migrate the entire store away from Client A’s instance.

We’ve separated it into its own instance, but what Client B would ultimately like to see is the store (and customer accounts, order histories, etc.) setup under the instance with the rest of their stores.

Any thoughts on the best way to go about this?