My recruiter started his email with phrase : I hope you're doing well.
Is it correct to reply : Thanks, I am doing well and I hope you're doing well too.
My recruiter started his email with phrase : I hope you're doing well.
Is it correct to reply : Thanks, I am doing well and I hope you're doing well too.
The grammar of your response is correct. However, pragmatically the question by your recruiter is quite possibly a polite formula, as Mike has hinted. The recruiter probably has little actual interest in your wellness, except as it might directly affect your ability to do your job. Therefore, you can consider the sentence as one that needs no response. Instead, you should get right to the matter that you want to tell the recruiter.