Bad news for you
The DNS-320 and DNS-320L use different filesystem formats. When you put a disk from the dns-320 into the dns-320l the disk will be recognized but you will be asked to reformat it. There is no way around it (unless you want to replace the firmware with a minimalist debian).
I used a PC and a second disk to first save all data from the dns-320 drive to the backup disk, then put the drive from the dns-320 in the dns-320l, reformat it and then transfer all files back from the second disk back on the newly formatted disk from the dns-320l using the PC again.
The copy process may take very very a long time depending on the size of your disk and if you only copy the files via ethernet. If you have a PC, i can only recommend to hook the dns-disk directly to a free sata port of the PC and copy the files using the PC only, not the dns. If you're on a Windows system you need to install
Ext2Fsd to be able to read from the ext2/3/4 filesystem partitions that the dns uses. Write access must be enabled manually in the tool's settings!