"Transfer my Data" supports transfer of SMS/MMS to/from SD card.

"Transfer my Data" is a free app that comes in handy when switching to a Lumia. Notice here that I do not say Windows Phone but Lumia because "Transfer my Data" is a Lumia exclusive. So if you're planning a switch to Lumia phones, add this app to your check list.

"Transfer my Data" has been designed to let you easily and smoothly transfer your contacts from almost any phones: Symbian, Android, iOS, Blackberry, Windows Phone and others. Some phones may also support transfer of text messages. That's what the app description says in the Windows Phone store and I do not know which phones are actually supported.

In the update published today, one of the new features listed is "Transferring text and MMS messages to and from an SD card". Support for MMS is a new addition. The second feature is the usual bug fixes.

"Transfer my Data" is free for download in the Windows Phone store.