This disorder used to be called factitious disorder by proxy or Munchausen syndrome by proxy.
Factitious disorder imposed on another is similar to factitious disorder imposed on self, except that people (usually caregivers, typically a parent) intentionally falsify or produce physical or psychologic symptoms in a person in their care (usually a child who is unable to contradict the caregiver's falsehoods or tell how the caregiver caused injury).
The caregiver falsifies history—for example, by stating that children have been having fevers or vomiting at home when they actually have been well. Some caregivers may even injure the child with drugs or other agents or add blood or bacterial contaminants to urine specimens to simulate disease. The caregiver seeks medical care for the child and appears to be deeply concerned and protective. The child typically has a history of frequent hospitalizations, usually for a variety of nonspecific symptoms, but no firm diagnosis was made. Such children may be seriously ill and sometimes die because of the caregiver's attempts to simulate an illness.
As with factitious disorder imposed of self, the caregiver has no obvious external incentives for the behavior. For example, the caregiver is not trying to cover up signs of child abuse.