If they have been split clean then the second file would lack the header information that F4M might require. Since VLC reads the stream data directly it can play it anyway.
Try combining the two files by opening Terminal.app, then write "cat [path/to/firstfile.ext] [path/to/secondfile.ext] > combined.ext" (without brackets/quotes; for the file paths you can just drag-and-drop the files onto the terminal window). The resulting file should appear in your home directory.