I would like to reply to a message that says, "I hope you are doing well," and I want to return the acknowledgement. Is it acceptable to reply, "I hope you are doing well, as well?"
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A simple, "Thank you, I'm well". But as someone who uses this expression at the start of some emails (only when I know the receiver and we're on more than formal, though less than friendly, terms) I don't actually expect a response.
A very common phrase used to inquire about the wellness of the message recipient is...
I hope this message finds you well.
This phrase behaves like a question, but reads like a statement.
However, according to the article Speaking Your Reader's Language (see paragraph 6 about e-mails to strangers), by Lynn Gaertner-Johnston, you may want to avoid using the phrase when sending a business e-mail. The act of inquiring how a stranger is by using the word you (at all) can be considered too informal.
This other article, also by Gaertner-Johnston, explains (see the third-to-last paragraph) how the phrase might have an awkward feeling about it, and gives a list of alternatives. However, I am confident that its use is still OK, as I have seen this being used numerous times even in the past year or two at both work and home.
Finally, here is a sample letter where the phrase is used (see the very first line).
I would say in response:
Thanks for your good wishes. I hope you are doing well, too. (I wouldn't repeat the word "well" as in the original example.)
You could say, "Thanks; same to you". They'll get the point.