The question is too bad, blame the people who made this ambiguous question.
Aaron Lee
I'm , I posted it for bump instantly.
この/この fits for the case where you are showing some pictures of the friend. この/その can be used in this case. その/その fits for the case where you mentioned the name of the friend before, and asked why you know him, and you are explaining it.
Therefore, その/この is wrong in any case, but others can be used and the most appropriate answer depends on the situation.
Oliver Nguyen
When it comes to this question, I'm thinking about which one is correct, lol.
この友達 sounds like you're pointing your finger at the friend in the picture and saying "this friend is the person who gets my Japanese thesis checked." It also sounds like the friend is in front of you and you're saying, "this person is the person who gets my Japanese thesis checked"
On the other hand, その友達 sounds like the friend was already mentioned in the context and you're saying "that friend is the person who gets my Japanese thesis checked"
その友達 can also be used when you've already met the friend or you already know of them. Sorry for the poorly written explanation in English, but what I want to say is that it's too ambiguous to answer as the different Japanese user already responded to you.
Is it not simply about specifying association? その being a way to explicitly state that it's the other person's friend, even though it's already implied. E.g. その友達 -> ”それ”(相手)の友達