I apologize in advance if this is confusing (this is the best way I could explain it):
Is there a way for the files Person B is sharing with Person A to be saved on Person A's computer so that when Person B goes to work, they still have access to the shared files, and then when they return home the files are re-synced with the shared folder? (Person A and B are both not very tech-savvy, which is why they were using Local Network Share in the first place.) Since Person B has the files that are to be shared with Person A, how does one sync files with Windows Samba share from within Ubuntu?
Just to clarify - there are no issues right now with Ubuntu-Windows interoperability - this is really a general question about caching (if that's the correct use of the word) the files on Person B's computer until they can return to the Local Network for the files to be updated.
I've successfully connected my Linux machine to a number of different Operating Systems using samba. I don't remember the exact software I used, but with some quick searching, I found a samba client in the Ubuntu Software browser called Smb4k. There are also command-line utilities you could use.
In my opinion, however, the better options both in terms of scalability, ease of use, and cross-platform compatibility is a program called Syncthing. There is a Windows exe, it's in the Ubuntu Software store, or can be downloaded via apt-get, and there's even a mobile app version for your smartphone. It functions much like Dropbox, except you maintain control of your own data. You can set it up to work only over your home network, or over the internet using Syncthing's relay servers.