Hi,
You can write those sentences in Korean like this.
안녕. 쉐인
annyeong.
마침내 만나게 되어서 반가워.
machimnae mannage doeeoseo bangawo.
엄마가 쉐인을 많이 사랑하셔서 쉐인을 많이 그리워하는 것 알고 있어.
eommaga sweineul mani saranghasyeoseo sweineul mani geuriwohaneun geot algo iseo.
엄마가 언제나 쉐인에 대한 이야기를 해 주어서 어머니가 쉐인을 많이 자랑스러워하는 걸 알 수 있었어.
swein eommaga eonjena sweine daehan iyagireul hae jueoseo eomeoniga sweineul mani jarangseureowohaneun geol ral su iseoseo.
집에 온 걸 환영한다, 아들!
jibe on geol hwannyeonghanda, adeul!
고마워.
gomawo.
하롤드가.
haroldeuga.
Since the letter is for your son, it is written in informal Korean.
There will be a lot of words and phrases to cover to let you know about those sentence. So, May I ask you check and tell me which word you would like to know the most? If I know your level of Korean, it will be much helpful to explain you about Korean : )
I hope you have great weekend.
Thanks!