The information in this question
Choose which Google Account when accessing Google Groups?
is no longer current
I am signed into Google and in Gmail click a link to an invitation made to another of my email addresses. I tried adding that email to the Gmail account as an alias, but the Google group in question did not let me in.
Must I ask the owner to resend to the Gmail account or can I sync/alias the other address to my Google account? I prefer to not use my main Gmail account for the list in question.
Best Answer
If you didn't yet added your desired email address as an alternate email address to your Google Account, do that first. See Sign in to your Google Account with another email address for details.
Then, go to the group membership settings, and change the email address to be used for that group.
From My membership settings - Google Groups Help