Thank you so much for your very prompt reply.
DOH! - There it all is, exactly as you described
Three experts (including me) in the office failed to spot this because we weren't looking for Gmail, rather trying to find it associated with the email account.
You are a force to be reckoned...
We are migrating from 2010 to 2013 and use the 'old' Gmail for Business aps as the Mail server.
This Free Gmail service is quite old and is no longer supported by Google because they want you to migrate to the paid Google Apps for Business.
For a variety of reasons we cant undertake to...