For e-mail, I use G-Mail through Apple Mail, and am having huge problems sending to a

E-mails from their address come through to my G-Mail/Apple Mail with no problems, but sending from G-Mail/Apple Mail doesn't show up in their Inbox/Junk, or, indeed anywhere.

Even trying from, doesn't show up in their end.

Do any forummers have any suggestions? It's driving me up the wall.