This is related to a topic I started years ago.
I was looking for a way to remove photos from one of those horrible sticky page albums. At the time I didn't get a good definitive answer, so I just let mom's albums on the shelf. But this morning, she had enough and told me to photograph the pictures she wanted to save. So, I did that; but knowing that they would go straight to the bin, I took a few of the pages she didn't want to keep to experiment. Am I glad I did!
I finally have a solution to removing the pictures without damaging them. I don't know if this would work as well with FB prints, but with the color photos that were there, it worked a treat.
So, here's the walkthrough. You will need an X-acto knife and a flat bottomed tray full of water. I just had some developing trays with some smooth gutters for the print tongues and it worked a treat.
First, you need to cut wide and deep around each picture with the knife (don't cut through though). Once this is done, take the point of the knife and start peeling apart the cardboard backing. This is important as you don't want to damage the print. Usually, the backing cardboard will have less holding power than the glue that holds the print in place. You can use the knive at a shallow angle to cut through the glue that holds both sides of the cardboard together (but don't cut right under a print!).
Second, put the prints one by one in the tray letting the cardboard drink-up as much as it will. The glue is actually water-soluble, so it softens as you wait. At one point the print will start separating from the glue, so you just pull smoothly and slowly. Sometimes the glue holds too much, but this is not a problem as you can start pulling from a different corner. If the cardboard leaves bits on the back of prints, you can just rub it off with your fingers.
Third, set the prints to dry.
That's it!
I managed to save a bunch of photos that way.
Hope you find it helpful