I'm trying to transfer my data from a Nokia Lumia 625 to a 635. According to different guides I should be able to transfer both contacts and SMS to the other phone but the option to select SMS never shows up. I can only transfer contacts and nothing else. I haven't found anything useful. Is this a known issue?
Have you tried enabling SMS Backup from settings -> backup -> Text messages? This will take care of uploading the SMSes backup and from the new phone you just turn on Message backup from the same settings -> backup -> Text messages and select "any time" for "Download messages from". This works fine for me over multiple phones. The best part is if you have multiple phones and multiple SIMs, it basically downloads all message from both phones on every other phone.