To service recipients from another domain in the AD Forest, you need to run setup /DomainPrep in that domain. This creates the necessary objects in that Domain and assigns the required permissions.
Next, you need to create a Recipient Update Service (RUS) for that domain, and point it to a Domain Controller (in that domain). RUS watches AD for new objects (recipients) or changes to existing ones, and applies Recipient Policies. This generates the email addresses and other relevant attributes required to mailbox-enable a user or mail-enable users and other types of objects (Distribution Groups, Contacts, etc.).
The following KnowledgeBase artcile has more details: KB 275294: Creating Exchange Recipient Update Service instances for remote domains.