Addressing other person's parents in Korean.
아버지, my father. 아버님, other's father
어머니, my mother. 어머님, other's mother
할아버지, my grandfather. 할아버님, other's grandfather.
할머니, my grandmother. 할머님, other's grandmother.
Although there are more formal words, like 모친, 자당, 부친, 춘부장, 춘당, in Korean Language, but those words are not used in modern society.
(the beginning)
사랑하는 OOO(your boy friend's name)씨의 부모님께.
(the greeting)
어머님, 아버님, 안녕하세요.
(the contents)
아드님에게 헝가리에서 일하며 공부할 기회를 주셔서 감사합니다.
Thank you, for giving the opportunity to your son to study and work in my country!"
너무 멀어 직접 찾아뵈올 수는 없기에, 다만, 이 선물을 보내 드립니다.
"Although we couldn't meet in person so far, I would like to send you these gifts from my country"
(the closing remarks)
2013년 OO월 OO일, 안나(Anna) 올림
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The manners of Korean towards the elder or the superior is always to be humble and to show respect to them and to use honorifics.