I need a proverb for a person who is poor in his native place and migrates to another country for better living, but there too, he still remains poor. So how can we call that person in proverb. In my own view, "a have not is a have not everywhere".
While I find no proverb/idiom that exactly addresses your concern, what Khan made seems to be the closest in this context.
poverty follows the poor everywhere
So, to write your story again...
Harry suffered from poverty. He made his mind to try his luck elsewhere. He moved to a city but there too poverty followed the poor.
I googled for "proverbs luck" and "bad luck proverbs" and found a chapter titled "Fortune and Luck in Proverbs", from D.E. Marvin, comp. "Curiosities in Proverbs", 1916.
Here are some examples
Every wind is against a leaky ship. (Danish).
By land or water the wind is ever in my face. (English).
He falls on his back and breaks his nose. (French, Italian, English).
He would break his neck upon a straw. (Italian).
“He would drown in a spoonful of water.” (Italian).
From another collection: (Robert Christy, 1887)
If I went to sea I should find it dry. (Italian)
If my father had made me a hatter men would have been born without heads. (Irish).
There's an Italian proverb that is antonymous to your requested proverb:
Who changes country changes luck.
You can modify it to:
A change of country brought no change of luck to him.