Step 1: Identify the direct speech.
Direct speech: She said, "Brother, I shall give you my watch."
Step 2: Conversion into indirect speech.
In indirect speech, the verb "shall" is changed to "would" for the past tense. Also, the pronouns are adjusted according to the speaker.
Indirect speech: She said that she would give him her watch.
Final Answer: \[ \boxed{\text{She said that she would give him her watch.}} \]