How to back up text messages on my iphone?

So like 3 days ago (i think) my phone got messed up, says there's no sim card, &&: it started turning on &&; off, so i took it to the store to get it fixed &&: they said they would have to delete everything. I have all pictures/videos saved already, but how do i back up my text messages?
&&: i connected my phone to itunes so i could back it up but how do i know if it backed up?-.
so if anyone could help thanks ( :

Added (1). I would do snapshots but its a long conversation -.

I'm not fully sure how to back up texts, but you can take screen shots and back the texts up as photos!