Forwarding SMS messages is a contractual relationship between telephone companies. Unlike a phone call (which is implicitly connected... as you want to actually use the phone), an SMS is not automatically forwarded. For instance, for a period of about two years T-mobile (USA) had no 'SMS forwarding agreement' with Vodafone Italy. As such, I could not send text messages to my sweetheart. Her SMS would come to me, but I could not reply... after setting up a Skype account to sent SMS on my behalf, I could do this but finally gave up and switched to AT&T. Eventually T-mobile found it useful to set up the agreement.
The problem is not with our phones. It is nearly impossible to get these answers from support people as they lack the ability to find any reference in their fixed list of responses. I happened to once get connected to an Italian support person who actually cared enough (and could) research the situation. Knowing messages would go one way, but not the other was stupefying.