Gmail: automatically respond to email from different email address

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I am currently using my Gmail account (say, good.morning@gmail.com) to manage several other non-Gmail email accounts (for example's sake, a@a.com and b@b.com). I have emails forwarded automatically from both of those other accounts into my Gmail account. For one of those email addresses (a@a.com), I am also able to send mail through Gmail, and my account is configured to automatically respond to all mail sent to a@a.com with an email from the same address.

Due to institutional policies governing b.com's email account (lack of SMTP access), I can forward mail to Gmail but am unable to send mail as b@b.com from my Gmail account. I would therefore like to reply to all mail sent to b@b.com with an email sent from my account a@a.com. Is there any way to do set that up automatically in Gmail?

Sorry so long.

Best Answer

In order to be able to respond an email with an external email address you need access to the SMTP servers of the external email address as Gmail policies doesn't allow to send email from external addresses from their own email servers for security reasons.

References
Send mail from a different address or alias - Gmail Help