From the pictures, it looks like it is floating in a carved out well (like a lot of Floyd Roses). Unfortunately, with my limited experience with FRs, this rules out flat loading it with lots of springs, like a Strat. Therefore, I imagine that you’d have to insert a couple of blocks of wood, either side of the string block to stop it moving back or forward. Once happy with their positioning, you could glue them in place. Hopefully, some wiser folk will chime in with a different solution.