Woody's recent article about moving to Gmail and no longer use Outlook, comes with an issue he does not address.
He said he moved his email and used his existing address seamlessly. However I find this is not possible as emails sent this way from Gmail display both the 'cloaked, address and the Gmail address.

My wife is using his approach.
When I receive her emails, the from address looks like this:

Jane@smith.com on behalf of Jane.smith@gmail.com.

This defeats the purpose for me. People now send email directly to the gmail address and it is entrenched now and immovable. So doing what Woody suggests would result in emails from him showing:

Woody (at) askywoody (dot) com on behalf of woody (at) gmail (dot) com

This is unacceptable to me. How can this be prevented and why did he not mention this?