How to get information back on to your iPhone?

My dad recently dropped his phone in to some water and his iPhone died, he got a new one and he hadn't backed anything up, he, my mom and i all share my iTunes account, he never synced his phone to the account. We went to "view my account" and then went to "purchase history" we can see all the purchases he made but we have no clue how to get it on to his new phone, is there a way we can do this? There isn't an option to download from where we can see all the purchases, its just a list of everything we've all downloaded on to our iPhones

ITunes?

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