Question

کار او پاسخ دادن به نامه ها است

...

Answer 1

His job is to answer the letters.

His job is answering the letters.

Her job is to respond to the letters.

Her job requires/entails answering the letters.

Answer 2

His task is to reply the letters.

Her duty is replying the letters.

With +1 for Mr.Hamzeluyi's answer

Answer 3

Hi,

This form can be used as well:

Anserwing/responding to letters is his job.