I have done this to a Ricordia Yuma before on accident, well intentionally because I had to move a rock. The piece that had no mouth grew a new mouth within the following days. Ricordia FL would be the same, with or without a mouth. I plan to cut mine so I can have a few.
Wait till the mouths are a little further apart from the main one. Oh yeah, my ric fl. split without developing a mouth but after it split it developed a new mouth. Some of my other rics have 2+ mouths and still have yet to split so dont get your hopes up, they tend to take a long time.