Yes, exactly as Oliver states.

Since this is your first visit to FRA, ask the LH Worldshop sales rep to include the VAT export documentation for you, when you pick-up your luggage.

I would pre-pay early as mentioned previously, examine your luggage when you arrive at FRA, and have the sales rep assist you in filing out the VAT export form correctly. I know this sounds like a simple task, but it might be an easier and positive experience for you, considering your short time table, possible jet-lag, and unfamiliarity with navigating around inside FRA for the first time.

Remember also to keep all your receipts and documentation in your purse with your passport and boarding pass, and not in the new luggage.