Infinitives of purpose
We can use an infinitive of purpose at the end of a clause to explain WHY we do something or did something:
- I came to London to learn English.
- I went to the shops to buy some milk.
- I am studying hard to go to university.
In the sentences above, why did I come to London? To learn English! Why did I go to the shops? To buy some milk! Why am I studying hard? To go to university! Notice that the infinitives of purpose here have no special relationship with the verb. They are Adjuncts. They give us extra information about the sentence and explain why someone did something.
Stop + --ing:
The verb stop can take an -ing clause as a Complement:
- I [stopped smoking].
- I [stopped running].
- I [stopped reading my book].
The -ing phrases above explain what action finished. So I finished smoking and running and reading my book. Sometimes we don't need to use an ing clause to explain what stopped, because the listener can already understand this:
- It was raining yesterday. Suddenly it stopped.
In the second sentence above we understand that it stopped raining. We don't have to use the verb raining a second time. Or consider this sentence:
- I stopped on my way home yesterday ...
In the sentence above, we understand something like stopped going home, or stopped walking or stopped driving. The exact action is not very important.
Using both things together:
So we can use a sentence with the verb stop with or without an -ing clause afterwards. Whether or not we use an -ing clause, we can also use an infinitive of purpose to explain why we stopped (doing something). So I can say:
- I stopped smoking to improve my health.
- I stopped eating to speak to my friend.
In the sentences above, if the listener knows I was already smoking or eating I could leave the -ing clause out:
- I stopped to improve my health.
- I stopped to speak to my friend.
Notice that the infinitives of purpose have no special relationship with the verb stop!!! They are just extra bits of information.
The Original Poster's Question:
- Ali stopped _____ to his friend. He talked to him right then.
I have added the word right to make the second sentence more natural. Now if Ali stopped talking, it means that the talking finished. But this is not possible because Ali talked to his friend! But if Ali stopped (doing something else) because he wanted to talk to his friend, then the two sentences make sense, because Ali did talk to his friend. This is why the infinitive of purpose to talk to his friend is the best answer.