A limitation exists where objects exported with the FBX format remain in the last state shown in the Viewport. The plug-in exports any vertex animation on an object in its current PRS coordinates. For example, if you export a cylinder with a 100-frame animated Bend modifier at frame 50, the scene shows the cylinder at a 50-percent bend.
To accommodate this limitation, position your time slider at the point in the animation you want to export. To retain the entire animation, create a selection set for animated objects. Then, activate the Include > Animation > Point Cache File(s) option in the 3ds Max FBX Exporter window.
