Simplest thing, while logged into the source FS:
rsync -avz --rsh=“ssh -l remote_user_name -p remote_port” /name/of/source/directory/ name.or_ip.of.destination:/name/of/destination/directory
You can also pull from the destination instead of pushing from the source, it’s up to you.
Replace remote_user_name, remote_port, name.or_ip.of.destination and /name/of/*/directory as applicable.
If you add a -n while you are doing initial testing it will do a “dry run” and tell you what would be transferred but not actually transfer anything. This can be useful while you are messing witth getting the right path, etc.
You will need to enter the remote password. Once you can get this to work there are ways to set up public/private key based secure logins using SSH so you won’t need the passwords any more.
From what I remember the directory names on the FS are a bit odd (/mnt/shares/something like that). I’m sure there is info on here somewhere.
To make it easier you should do some sort of dynamic DNS so there is a DNS name for the destination. Try http://www.dyndns.com if you don’t already have a solution.