Throughout Absorb's many message templates, you have the option as an administrator to enable the Send to administrators toggle as can be seen below.
With this toggle enabled, all administrators who have their User Management set to DEPARTMENT or GROUP will be copied on the message, including the department administrator for the user in question. Please note that with this toggle enabled that the message is not exclusively sent to only the direct department administrator - the email will be copied to all admins that oversee this department. However, these messages will not be be sent to admins who have their User Management set to ALL.
For more information about settings such as these, please see our knowledge base article called Message Templates.