You can back them up to a GMail account from your BlackBerry via a program like DexRex, but getting them into the iPhone is not going to happen. You can transfer text messages from an old BlackBerry to a new BlackBerry via BB Desktop Manager. You can transfer text messages from an old iPhone to a new iPhone via iCloud backups. But cross-platform sms transfer doesn't work for anybody.
You need to transfer SMS text messages from iPhone to Blackberry via a program, too.
Last edited by derrickjuarez; 04-16-14 at 09:14 PM.