The correct answer is:
A. He is believed to have won a lot of money on the lottery.

Explanation:
The sentence is in the passive voice and suggests that people believe something about the past (that he won a lot of money). "He is believed to have won" indicates that the belief is about an event that happened before now. This is the proper structure to convey the idea that people think he won money in the past.
 
 
 
 

The correct answer is:
A. He is believed to have won a lot of money on the lottery.

Explanation:
The sentence is in the passive voice and suggests that people believe something about the past (that he won a lot of money). "He is believed to have won" indicates that the belief is about an event that happened before now. This is the proper structure to convey the idea that people think he won money in the past.
 

The best option that correctly rephrases "People believed he won a lot of money on the lottery" is:

A. He is believed to have won a lot of money on the lottery.

This option maintains the original meaning and uses the correct grammatical structure.