Verbo "become" no present perfect continuous

No, become + ING doesn´t exist to continuous verbs. It´s a stative verb.

But "Becoming" do exist when it is a dynamic verb.

The thing is, becomes is a stative verb in the sentence:
He becomes easily irritated
You can see that he is getting irritated, so you can make this statement - you can´t say he´s becoming because one is talking about "how things are" with him. It´s not a change in him, we are seeing something that is commonplace, it´s his way of being (almost of a trait of him.)

So, when we are talking about the "state" in which he gets irritated, we use "becomes''. Here you can´t place (time) when his irritated state begins, he may have begun to be irritated before with something else that triggers this state.
So, "become" with states (hate, love, etc) will be like this, it doesn´t take the ING form.

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Now you are saying "he is becoming an expert", you can say that, and it has to do the "process" of becoming/getting an expert.
So, to processes you can use "becoming".

Those three days, while important for school, are crucial for me. For us.
I need those three extra days to watch him play. To hold his hand. To listen to his stories. And to revel in the boy he is and the man he is becoming.
That are the words of a mother, so she´s clearly talking about a process (the one of - becoming a man), not the state.
There´s no such a thing as a state of becoming a man...

http://www.edufind.com/english-grammar/ ... ous-tense/
http://thegrammarexchange.infopop.cc/ev ... 6306002132
http://kristinsb.com/2015/08/18/the-man-he-is-becoming/

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Some English verbs, which we call state, non-continuous or stative verbs, aren't used in continuous tenses
http://www.perfect-english-grammar.com/ ... verbs.html

That´s why I initiated the answer with a "no", when "becomes'' is a stative verb it doesn´t can be continuous. When you see it "becoming" it certainly will be in his dynamic form (the case above, "becoming a man" is something dynamic), not stative, not a feeling or something...

Obrigado, Paulo, pelo interesse em detalhar. Sua resposta me convenceu de que become é semelhante ao 'tornar-se', um verbo de ligação que pode ser mais do que um simples verbo de ligação. Por isso acho que posso dizer This country has been becoming poorer = Este país está se tornando mais pobre. Tô certo?

You got it right, grammatically speaking. And the sentence is grammatically correct as it is.

As for the poverty process, yes, depending on what one thinks when stating that. A country or people can be poor without being in the sense of lacking material possessions, like they say it´s all in one´s head (and somehow, a little bit on culture). One thing is certain, (true) education is a powerful antidote against poverty, injustice, misinformation, and a lot of other ills of any given society.
Education empowers and knowledge is power! and it´s obvious that if people are empowered, not only a few, any given country will develop, and even when it meets some bumps, it will bounce back in no time, fast, quickly.
Honestly, even in times of fat cows - the good times - we have a certain culture of the moneyed takes it all. Please, guys, don´t get me wrong, but sometimes we have that impression that something is amiss...when we see so many things, injustice, death, corruption, monopolies, etc, that it´s hard not to think that something is upside down.
Being an optimistic, I hope that soon we will see, or will sometime see things straightened out. Anyway, I can assure you that education and information will play a role in it. I have a dream...