you can follow the below steps to start your own transferring process.
1. Enable USB Debugging.you need to open the USB debugging and install a USB Driver on your Samsung phone by following the instructions on the interface.\
2.Directly click "Contacts" button on the top of the panel, then you'll find there is a "SMS" option existing in the left panel. -
3.Export and Save SMS on Your PC
For more details in support option of Samsung India website.
"You’ll normally and usually do need to Backup data on your Android when making changes to your phone or changing your Smartphone in order to move your existing data to micro sd card, PC or cloud storage services, so that you’re able to restore it safely and successfully in times of need. There are plenty of App on Play Store which offers to easily do it. I have searched and reviewed a number of apps and finally have come up with following top 5 list."
For quite a while, the gold standard for SMS backup has been SMS Backup & Restore by Ritesh Sahu (FREE - Google Play). There are other free SMS backup apps available on Google Play that also have good feedback, including SMS Backup, SMS Backup +, and Super Backup: SMS.
There is absolutely no need to pay for a backup app, when there are so many good, free options available.