Hi,
I'm afraid, this kind of data is being used just internally within the plug-in and exported instances don't inherit it - any of Forest Pack's Animation modes doesn't animate the used object itself - it gets the animation samples from the source object, i.e. animated meshes or procedural object as GrowFX.
It's possible to get Forest values (like animSample & animOffset) by using the Forest Exporter tool > export them to a .XML file and though this tool is developed mainly to be used in advanced pipelines and to aid interoperability between software it might be helpful for this task.
Best regards,