I've figured out about half of the problem this time. I've duplicated the directory structure of the Windows machine on the Linux server.
I then proceed with mounting the Windows share on the Linux server. I type the mount command while I'm in Folder1 on the Linux server:
mount -t smbfs -o username=test,password=test //192.168.1.3/Folder1/Subfolder Subfolder
So far so good. Now I need to rsync and the command for this is
rsync -va /path/to/src /path/to/dst
But what do I fill in here? I'm guessing path/to/dst is just plain Folder1 on the Linux box. Path/to/src refers to the share on the Windows machine but since I've mounted that share, is path to source = path to destination?