"in response to" vs "for response to"?

Solution 1:

In this scenario, response is referring to "a verbal or written answer" or, simply, "a reaction":

response

• a verbal or written answer: we received 400 applications in response to one job ad.
• a reaction to something: an honors degree course in Japanese has been established in response to an increasing demand.

The preposition in is therefore more suitable:

in

3. indicating a state, situation, or condition ⇒ in a deep sleep, standing in silence

If you are a native speaker of English or you've familiarized yourself with linguistic expressions in English (by reading many English books and listening to many English podcasts, etc), you can tell straight away that the expression writing for response simply makes no sense.