Is it impossible to assign a manager from a different domain in Active Directory to a user in another domain?

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No, it is not impossible to assign a manager from a different domain in Active Directory to a user in another domain, but it requires some additional configuration and trust relationships between the domains. This can be done through cross-forest trusts, which allow users from one domain to access resources in another domain. Once the trust is established, the manager from the different domain can be assigned to the user in the other domain. However, managing and maintaining cross-forest trusts can be complex and requires careful planning and implementation.