I used to have an old Moto G1 that ran Kit Kat, 4.4.4 (it was definitely Kit Kat but I might be off on the exact version...), but I initially had the same problem and searching this forum I finally found that Google had made changes to the Android OS that limited what could be moved from the internal memory to the external memory provided by the SD card. It was done in the name of device security and also Android's attempt then to move to all inclusive devices that didn't use SD card slots but all it did was create a big outcry as users coming from then older Android OS's suddenly couldn't move files they had been accustomed to. There never really was a way to solve this entirely, some people had better success than others with some of the file managers in the Play Store or a PC.
I myself when I first powered on my Moto G1, I also was using a brand new and large capacity SD card, so it wasn't as if I had all my music and pictures already on the SD card and it'd be a simple swap from an old device to a new device. As I was then using a device management program to move music from my PC onto the device, it filled the internal memory and I ended up with less than a megabyte of internal memory and a whopping 32gigs of SD card space. I had to fight with it and eventually take it back to the place I purchased it and they helped me.
If it's apps that you're looking to move you'll likely only be able to move the apps that the creator of said app has decided to give you the option of moving. Otherwise if it's some other types of files - music or pictures for example - you may have to use a PC to do it. Perhaps using the PC's file explorer, find the file in the internal memory, move it to the PC as a way point and then move it to where you want on the SD card. Google's decision was less than popular and it became less restrictive as a response with subsequent Android OS's.
