Answer:
True.
Step-by-step explanation:
The text above shows exactly the concept of extended metaphor, as an analogy that runs through the whole narrative in a very subjective way, but that establishes the theme and the message behind the story well. In other words, an extended metaphor is a metaphor supported throughout the text.
The text shown in the question above also correctly presents how the concept of extended metaphor is placed in “there's a man in the habit of hitting me on the head with an umbrella”, when non-literally compares this unforgettable moment in something that provided comfort and stability to the narrator of the story.