If I replace my iPhone 4 can I get my pictures and stuff back onto it?

My lock button recently got stuck. So I might be getting it replaced at the closest Verizon store. If I do, can they somehow get all my pictures, apps, and contacts onto it somehow?

You can always redownload apps onto different devices as long as you you have bought it on one device. To get your music and pictures, you should back it up on your computer before replacement of your phone, or back it up on iCloud.
https://www.icloud.com/...cloud.com/

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