IPhone 4 - transfer all content to new phone?

Hello,
My iPhone 4 was accidentally dropped in the sink and was exposed to clean water for a second or two. I immediately fished it out and dried it off with a towel. The phone (screen, buttons) was working, though the sound was no longer working.
I switched the phone off and followed advice to cover the phone in rice to draw out the moisture. It's been covered for 24 hrs, I am waiting another day or two before I dare to switch it on.
I am worried that even though the phone seemed to be working, it might be damaged and suddenly stop working. I want to get a new phone, same kind.
The old one was backed up via iTunes to my laptop.
My question is: if I get a new phone, is there a way I can transfer everything that was backed up from the old phone to iTunes, to the new phone?
I am talking messages, pictures, music, contacts, notes, the works, like a replica.
If yes, how?
Thank you.
Kind regards

See:
iOS: Transferring information from your current iPhone, iPad, or iPod touch to a new device

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