Shit, I thought you don't have any messages on your MMC. Why don't you save your messages on a txt file? There is an app called Message Saver (freeware) which allows to save your messages in a txt file viewable both in phone and PC.
The trouble is that the messages cannot be appended if they are different in phone and MMC. When you select one of theese memories and you have different messages on them, you won't be able to append them. So the only way to keep them is either how you did it, or with that app.
Do you like my signature?