european iphone in australia can't connect to internet

My girl is now in Australia. She bought an iPhone 4 in Italy some years ago. when she put the Australian operetor sim the phone can connect to the internet (both 2g and 3g networks). Come to apple store they didn't fix the problem also because simply resetting the phone all go ok but when she restore it from the last backup internet connection doesn't work no more.

network settings reset doesn't work.

it's a problem of the phone cause she has tried 2 different carriers.

how can we fix that?

thanks so much