Step 1: Recall the medico-legal vocabulary. The label posthumous child is a defined term used in inheritance and forensic contexts.
Step 2: Apply the meaning. It denotes an infant who was already conceived while the father was alive but is delivered only after the father has died.
Step 3: Match to the choices. The option stating the child is delivered after the death of the biological father is the exact definition.
Step 4: Dismiss the others. Death of the mother, death of both parents, or abandonment each describe different scenarios and none matches the established definition of a posthumous child.
\[\boxed{\text{Delivered after death of biological father}}\]