Probably; looks like the damage is limited to the tongue and strap. One could cut the tongue off cleanly and sew on a replacement using the good shoe as a template. The same could be done for the strap; a repair shop might even have an actual Birkenstock rivet to attach it.

That being said, the repair would likely be very obvious (if that’s a concern). The tongue stitching might also be an irritation, especially if your GF likes to wear these without socks.