Moving of Text Messages from Android to Iphone

Yes it will move. But you can't do partial move.

Here's what gets transferred: contacts, message history, camera photos and videos, web bookmarks, mail accounts, and calendars. If they're available on both Google Play and the App Store, some of your free apps will also transfer. After the transfer completes, you can download any free apps that were matched from the App Store.

Move to iOS does move messages. It's bugged as ****, it's laggy, but you have all chances to make it work in 3-5 tries. Restart Android and iPhone, restart Wi-Fi router, make sure that both phones are connected to the same Wi-Fi router (IMPORTANT!!!!) and try to transfer data.