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Could you just contact him and tell him that someone contacted you at your home email address as they thought you left your job but got a work email from you, and then let him know that if he could sign his name to the emails you would appreciate it? If you were alerted to what was happening from an outside person, it seems like you could leave out the part about how you can still access the accounts.
When someone leaves our company, we keep their email active for a year I think, or at least we used to. I used to handle one of the email addresses, but whenever I replied to an email from her account, I always stated that the person no longer works here and that I was the person to contact going forward.