Well there are a few ways. The most direct being ...
1. Using the phone's "File Manager" app. If there isn't one installed, you can find them on google play store. Through this app you can move files from a SD card to the phone, or from the phone to the SD card. The only disadvantage is that it can take a while, depending on how many files you have, as it really doesn't do the move all at once thing.
2. You can connect the phone to a computer, via USB cord, while the SD card is in it. Then copy all the files over to an empty folder on the computer. Once moved, then you can copy/move them all over to the phone itself. This one is faster, as you can move all at once. Plus you can back up to the computer at the same time.
NOTE: You should make sure there is enough space on the device first before trying this.