After copying them, I'd soak the photo+glass in as shallow water as necessary to cover the paper. A deep tray might cause the dry paper to float and the glass to sink ripping it apart. No rush or harm in a good long soak, IMHO.

Normal methods for drying FB paper apply.

If it's been touched up on the print, the soaking might harm that, depending on how the touchup was done, thus an interest in copying it.

That's a nice trifold frame, but something with a window mat would be better for the future to keep the photo off the glass.