How to move a Third Person Controller with a moving platform?

I want to create a simple jump and run game using the 3rd Person Controller from the Standard Assets. The player has to use moving platforms to cross between parts of the level.

I can not figure how to move the 3rd person character with the moving platform it is standing on. The platform moves but character remains where it is.

As soon as the player jumps on a moving platform I want to transport the character with platform.

I tried to use CharacterMotor.js for the moving platform but that does not seem to help at all.

How get the character transported with the moving platform?