You can actually transfer content without using any application that requires payment. Unlike the iPhone, the Android is much more flexible when it comes to manipulate the data. For example, you can copy music, videos, images, and all custom content by simply plugging the phone to PC and enable USB transfer then copy the data from DCIM folder (images), Music (music), Downloads (custom files), etc. To transfer the contacts, simply sync them to the Gmail account and add that account to iOS and then sync the contacts to your Apple account. To transfer the mentioned items, install iTunes and add them like you would normally do.
Additionally, you can use the Move to iOS application provided by Apple: https://support.apple.com/en-us/HT201196
There you go, all the content has been moved without apps that require money. I have used this method a couple of times and it has never failed me.