The safest, simplest and easiest way is to use Vaulty's online backup. Media hidden in Vaulty is saved on your device and depending on your device and your settings it could save to your SD card. When you upgrade or replace your SD card you may need to transfer your vault from your old SD card to your new one. When using online backup, your files are saved securely online and automatically download to your new device.
If you don't want to backup your files online, you will need to transfer your vault manually to your new phone.