Gmail – How to Receive Gmail Inbox Activity Summary at a Different Email Address

Here's an idea:

1. Create another gmail account ("new account").
2. Add the old address to the new account so you can send mail from it.
3. Make it the default account.
4. Create an auto responder on the new account, which has the text you want to send to the users.
5. Create a rule on the new account which trashes all messages that shouldn't get this reply.
6. Set up the old account to read the mail from the old account via POP3.

As the mail is read in the new account, the ones that shouldn't receive a reply should be trashed and only the valid ones should go through (if this part doesn't work, you will need a 3rd account which forwards to the second based on a rule). Next, the mail that does go through should get auto replied via the auto responder, which should use your old account to reply.

Note: As you probably guessed, I haven't tried this. I would recommend trying it out first. Another problem that might happen is this new account might be revealed to the people getting the message via an "on behalf of message".

If you're using a filter you can set the filter to be the following:

to(*@gmail.com) as opposed to to(one@gmail.com)

That will catch any email that gets in your inbox, where one@ will only catch those to one@.

If you're using the settings > Fowarding and pop/imap it should forward anything in your inbox to that number.