onenote invites not being sent to external email addresses

OK.

We have Office 365. However, our email is currently hosted by an external provider. This will chnage, but not now. We use Onenote 365. Problem is, when I share a notebook with a collegue within the organisation, the email invite goes to their 365 email (rarely/never accessed) inbox/account; rather than their external email account. Ideally I need the email to go to their external email account.

For your info, the external email address and 365 login details are the same for each employee. Perhaps this is the issue?

thoughts welcomed