"Will you write me a letter?"

Translation: 저에게 편지를 쓸 것입니까?

[AndrejStas]

"저에게 편지를 쓸 것입니까?"

쓸 - is not amongst the options when making the sentence.

[SivaniLloy]

when you lont have the 저 에게 listed as an option are we supposed to hand type it? I thought you were trying to see if it could be implied?

[Doldrumz]

Could 써줄 겁니까 work as well ?