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You can do this via Kies which is a free program supplied by Samsung to be run on your computer.
To do this, download Kies from my link below pleasewww.samsung.com/us/kies/
Once installed, open it and connect the S4 and S6 to your computer
Click the Back up/Restore tab.
Click the device's name in the left panel you want to transfer content from.
Click Transfer between devices.
Click the drop-down box next to Transfer to another device, and select a target device.
Mark the content you want to transfer (eg: Contacts), and click the Send button.
Kies may display a notification when transferred information will result in duplicated content. Select the desired options and click OK.
Click Complete when the transfer is finished.
This will complete the process.
I can also do these steps for you, and have made a request via Additional Services. This is optional, and if you choose to do this, I can, with your permission, remote into your computer while you watch and do all these steps (and deal with any problems that arise during them) for you. Or if you do not choose to take this service, we can continue here. This is no problem at all.
Let me know the results please