From Trek to Surly - advice on frame size
You could compare the geometries of the FX and the Cross Check. Matching the standover, 56cm matches. Comparing the effective top tube lengths, between 58cm and 60cm match.

Bottom line the geometries are different.

On another note, the FX doesn't seem to be a particularly high-end bike, so purchasing a complete Surly could possibly provide more economical than moving the parts to a new frame.