abused muslim couple are ` hardworking , honest and kind '
they moved from pakistan years ago for a better life in australia .
stacey eden , 23 , stood up for them as woman launched train rant .
mr and mrs batthi 's mosque have made her an extraordinarily kind offer .
they will pay for her to visit the gold coast and their mosque for a day .
police sources have confirmed an investigation ` definitely ' underway .
the identity of the ranter remains unknown .