Change narration: The mother said to her son, "May you be successful".

The mother prayed that his son might be successful

The mother prayed by her son might be successful

The mother prayed that her son might be successful

The mother prayed that her son may be successful

The sentence is an optative sentence (expressing a wish), and "May you" changes to "might" in indirect speech.

The pronoun "her" replaces "your" to maintain proper narration.