Pass all elements in existing array to xargs
When you do
echo ${FILES[@]} | xargs -i mv '{}' /path/to/destinationxargs treats the entire line as a singe argument. You should split each element of the array to a new line, and then xargs should work as expected:
printf "%s\n" "${FILES[@]}" | xargs -i mv '{}' /path/to/destinationOr if your filenames can contain newlines, you can do
printf "%s\0" "${FILES[@]}" | xargs -0 -i mv '{}' /path/to/destination