Wow, lots of unnecessary complexity here in the attempted answers.
In any Finder window, look in the sidebar on the left. See the section called "Shared"? Your boyfriend's computer will show up there (assuming it also has File Sharing turned on). Click on it, and you'll be presented with one or two folders on his computer that you can transfer files to without signing in (the Public Drop Box folder for his account). You can simply drag the files and drop them onto that folder and they'll be copied over the network into that folder. If you want to be more specific about where they end up, you can click Connect As at the top of the window to log in with a username/password for his computer and put them anywhere you want.
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jW