Thanks for the quick response!
Unfortunately, by just specifying a single target folder in SharePoint, I lose the file's original path in box.
For example, if the file from Box is in folder \Dir1\Dir2\Dir3\FileName, the method you specify would lose the original path. All the files, regardless of their source path, would all end up in the same SharePoint folder.
What I'm trying to do is copy new files in Box to SharePoint and maintain the same relative paths in SharePoint. In the above example, the folder path in SharePoint would also be \Dir1\Dir2\Dir3\FileName (under, let's say, \Shared Documents).
My impression is that there's no current way to do that.
Thanks again.