Back in 2009 I wrote a post on SMS Forwarding and that I'd really like to have this feature to reduce the number of devices I carry with me. I did find an application then that I still use but it runs on the phone that forwards the SMS and not in the network, so not an ideal solution for me.
The issue with SMS forwarding by the network is the way SMS works in cross network and roaming scenarios. Let's say you are subscriber of network A roaming abroad in network B. Now a person who subscribes to network C wants to send you an SMS. The SMS architecture as initially designed would forward the SMS directly from network C to network B, so you're home network operator (A) never sees the SMS and hence can't forward it.
But lately I've become aware of a solution called SMS Home Routing, described in 3GPP TR 23.840 and some further background is given on Wikipedia. Not specifically built for this very purpose it could nevertheless be used by network operators as a basis for offering enhanced SMS services such as SMS forwarding. Very interesting! The TR was written in 2007 so there has been some time now for developments and deployments. From the outside, it's pretty difficult to tell, however, if the solution has found traction in the market.