to Uly: why "he's made" and not "had made"?

If I'm not mistaken, the Russian could be interpreted as a present eventuality or a past, no?

I'm not sure if I got your question right, but we have the action in past "сделал", and we have indirect speech. So, binding them both together we get to the past perfect tense, no?

What I meant is that the original Russian sentence can be interpreted in two ways depending on the situation: (this morning) He told me he's made progress in English. -or- (last year, after his trip to New York) He told me he had made progress in English. Is that right?

If I wanted to say that progress in English was done "this morning", I would specify it with something like "за сегодняшнее утро." Otherwise, I would assume that the progress was made during some time preceding TODAY or NOW. But! Shouldn't the past perfect be used in indirect speech regardless when it happened, as long as it happened before someone said about it?

¿Are both of these correct: (1) Сегодня утром мы с Андреем завтракали вместе. Я спросил у него, как проходят занятия по английскому и он сказал, что сделал успехи в английском и теперь понимает больше. (2) В прошлом году Андрей работал шесть месяцев в Англии. Я заметил, что он очень свободно говорит и он сказал, что сделал успехи в английском.

In English they would be: (1) This morning I had breakfast with Andy. I asked him how his English classes are going and he told me he's made progress in English. (2) Last year, Andy worked in England for six months. I noticed that he was speaking very fast and he told me he'd made progress in English.

Basically, they are both correct. I should've mentioned before, that the words "сделал успехи " sound unnatural to begin with, as if some of the Russian -Brooklynites said it. )) In both of your examples I would use "добился успехов". It sounds much better.

I'm confused about your sentence(1) in English. From what I know, the way to go from direct speech to indirect is as follow:
He said, - "I've made progress in English." - He said he'd made progress in English"
I just went through my Azar's English Grammar. Not a single example of use of present perfect in indirect speech.

The fact is that if what you're reporting is still true and valid in the present, then you can use a present tense. In this case, we're talking about progress, which refers to a gradual movement towards success. If you report about someone's status at any point during that movement, you can use the present. For instance, say there's a nazi hunter looking for a specific war criminal. In one interview he "tells the reporter that he's made progress in finding..." This is possible because the search is still ongoing. It's still valid and true in the present. http://usatoday30.usatoday.com/news/topstories/2008-07-17-720533519_x.htm

In this example, your man has made progress in English and is going to continue to study and make more progress: "I asked him how his English classes are going and he told me HE'S MADE PROGRESS in English."

I hope this makes sense. If not, ask me and I'll give you more examples.

It does make sense. Thank you! Just one more thing. Would it be correct to use past perfect in the same situation without any change in meaning? Would both of them "..said Thursday he'S made progress in.." and "..said Thursday he'D made progress in.." have the same meaning? Or, the use of "he'S" in this particular situation is still preferable for the reason you explained above?

Yes, you can say: On Thursday, Aleh told me he's made progress in English" because it doesn't matter when you said it - it's valid NOW.

Here's an interesting article. Look at the very bottom and it will tell you when you don't need to change tenses in reported speech.

http://www.ef.edu/english-resources/english-grammar/tense-changes-when-using-reported-speech/

Thanks again!

It s like one more discovery here. Nothing of the kind in the coursebooks. Thank you, Uly.

My pleasure, Tatiana :)