Just wanted to say, that after hours of searching, I finally managed to see my messages in Outlook.com . I am in Belgium, had automatic back up for my messages. Screen broken, and I do not want to buy another Windows Phone... Here is what helped me: (copied from other thread)
Hi Guys,
So if your "Message History" folder is gone, you are going to have to use "Categories" on the bottom left (or Quick Views).
Click on the "Settings" gear on the top right (near your name).
Select "Manage Categories" from the drop down menu.
You will have a lot to choose from, but put check boxes in "Contacts" and "Photos".
Now click on the Outlook.com on the top left, this should bring you back to your inbox.
Now you should notice the Categories in the bottom left hand side. Click on either Contacts or Photos
If you dont see anything, in the top right, click on "Arrange By" and make sure it is set to "Conversation".
It is the last part, the setting to "conversation" that made the difference!! All your messages will show up. Mixed with FB messages, but who cares. And now the tedious task of printing page by page of those messages. Bye bye Windows Phone!