Phone Transfer, the awesome transfer tools to transfer SMS from iPhone 5 to iPhone SE, helps you copy SMS between iPhones in batches. With only two simple steps, you can transfer SMS/MMS to your new iPhone with ease.
Mobile SMS Manager – copy messages from iPhone to iPhone
Only with this outstanding iPhone data transfer software can you transfer messages from iPhone 5 to iPhone SE. The steps on transferring messages between iPhones are simple as shown below.
First thing first, please download Phone Transfer on your computer and install it. You are able to use the free trial version to see how excellent it is before your purchase.

Step 2 Connect both iPhone 5 and iPhone SE on PC
After the installation, you will be guided to connect both your iPhones to one computer with USB cords. Within a while, your iDevices is to be detected. A box reading “Clear data before copy” will be shown in the bottom right corner. Click it if you want to wipe your iPhone 6 Plus data before the copying.

Note: If your iPhones are not on the right place, iPhone 5 on the left as the source device and iPhone SE on the right as the destination one, you can click “Flip” between them to change their position.
Step 3 Transfer SMS from iPhone to iPhone
Now, as everything is ready, you can check the data type you want. In this case, as you want to transfer SMS from iPhone to iPhone, you can tick the box next to the “Text Messages” and click the blue “Start Copy” button at the bottom to start the transfer process. And just wait for the end patiently. And the transfer is done when the progressing bar is filled.

It is very simple, isn’t it? You can also tick the music, photos, and other data type as you wish and they will all be transferred to your iPhone SE at the same time. You may perform the same procedures on iPhone 6 or 6s. If you have any difficulties on using Phone Transfer, please feel free to turn to us for help. We will always be here for help. Have a nice day.