This article explains that members must change their own email addresses or for the moderator to remove the old email address and add the new email address to the group.

There is not an option for moderators to make changes to a members email address. The member will need to log-in to their Groups Email Preferences section to make changes to their email address. 

If the member is unable to log-in to their account in order to make changes, another option would be for the moderator to remove the member from the group and then add the new email address to the group. Here is a link if you are unsure how to add members to your group.