I am not sure, cause if the deleted text messages were overwritten, it's impossible to recover them back. Just try phone data recovery scan your phone, if the deleted text messages can be scanned out, they will be displayed. Then you can choose them ...
Usually, such tool needs you to root your phone to recover deleted contacts and text messages. You can check the details on their pages. If no needed, maybe you deleted text messages were overwritten by new data. In that case, it's impossible to reco...
Actually, if they are both in your hands, the easy way to transfer data (contacts, images, etc) from old Samsung Galaxy Ace 2 to new Xiaomi phone is using mobile phone transfer tool. With itshelp, you can transfer data like app, contacts, sms, music,...