The correct option is
A He made out his money to a stranger.
The given sentence means that the subject gave all his money to a stranger. In the answer, the subject and the object remains the same. Thus, the rest of the phrase must mean 'gave all'.Option A is incorrect. Here 'made up' means 'formed' and not 'gave'. Thus, it does not have the required meaning and is not the correct answer.
Option B is correct. In the given sentence, 'made out' means 'gave as payment'. Thus, it has the required money and indicates that the subject gave all his money to a stranger. Thus, it is correct.
Option C is incorrect. In the given sentence, the phrase 'made off with his money' means 'ran away with his money'. Since the subject did not run away with the money, it does not have the correct meaning.
Option D is incorrect. Here 'made his money over' means 'made his money new'. This does not have the correct meaning and does not make any sense. Thus, it is incorrect.