Is it moral get free benefits from a country and then leave it for a better life?

'Leaving' and 'better life' are the two terms that make this question rather subjective.

You can leave your native country for study purpose or for other good purposes and then return and lead a better life as many people do. Often this can be treated as moral. But we can't admit intellectual and moral betrayal. It is always immoral.

If your question is about migration it may come under either moral or immoral, if you could differentiate them clearly. It completely depends upon the activity done after your migration. You needn't have to treat it as amoral.

While leading a selfish life in your new country you may say that you are leading a better life. This also is completely immoral.

If you realize that leaving is better than living in your native country, you may do so and lead there a better life throwing light to the whole world (I mean, giving great contributions to the whole world). If so, it is completely moral.

You are obliged to return what you received from your native country (your native country is also a part of this world). When you throw light to the whole world your activity becomes moral. As you mentioned in the question a few people might have done harm to her (I believe that might be the reason for the intellectual and moral betrayal, though it is not mentioned directly). But that is not an excuse for an activity done against a country. A normal person will not feel any repentance for leaving his country for a good purpose. Since it will not badly affect the person's spiritual development there is no need to have a feeling of guilt. So we can confirm that it is moral. This may be a matter of our unnoticed path of socialism; but never a matter of capitalism.

Review the concept of morals, and review your economy concepts, because you're subjectively implying a lot.

Morals is a system of regulation like religion or law, which ultimate goal is improving the survival probabilities of the group. Economy is not a zero-sum game, that is, living in a country is normally a win-win (except when you're clearly destructive for the country, or the country is destroying you).

So, your question reduces to "Do I decrease the survival probabilities of a group living in a zone if I move to another zone?" Probably not, because the impact caused by your change is global (you decrease the probability in one group but increase the probability in another, which will ultimately impact the first in a positive fashion; basically because you still exist and improve the probability of existence of humans, which prevails against the mental idea of borders).