Wow. That takes me back quite a few years as I shut mine down for good in 2010. That version of phonemail is basically a 80386-20 PC and it is running a slightly modified version of DOS and is limited in what it can do. I know you can backup all the settings and recorded names to floppy disks, but I'm not sure if you can back up the actual messages - if you could that would probably be a huge number of disks!
I don't know where you are as far as knowledge, but beyond the regular sysadmin login you can also login as tech with a password of field. Please note this is an extremely different command environment and it takes quite a bit of getting used to. There are a lot more low level things you can do in there, including accidentally wiping out your whole system, fixupdatabase, etc so be REALLY careful and don't say I didn't warn you. At the initial prompt you get after you login (it may be a SVI prompt) I believe you hit "c" to connect to the portal. I think you can use the "?" to list the available commands - most of them can be entered by only using enough letters to make it unique. If you want to get the system admin shell you may be more familiar with you can enter something like sysadmsh or something like that. There is one more password level even higher than that but I don't remember what it is anymore.
Sorry, that's the most I can remember, and if you already knew all that - sorry that's the best I can give you.