Lost luggage at frankfurt airport

Hmm.

Okay, I will "ask" - how did you forget your luggage? Were you rushing to a tight connection? Were you distracted by family or friends? Did you have a carry on and a personal item?

The airline/airport gave you the answer - they are willing to ship your bag to you at "triple the cost" of your admitted value. So, if there is nothing of sentiment or real value, as you say, "it's $80," then perhaps you need to cut your loss.

Or, if they will ship the contents only at 185€ (Euro) and you want to pay that, then it is your decision. If I am understanding your post, the luggage and contents would cost 247€.

Sorry for your misfortune. Would the airport ship only items of high value (and discard the rest)? That might be cheaper to send.

Should you ever lose anything on the rail network, you might do better -
The Secret Afterlife of Lost German Luggage

International shipping is expensive. Plus the airport will undoubtedly charge extra for their time required to prepare and ship the item. If it is only worth $80, then forget it and replace the items lost.

Anytime someone forgets a piece of luggage or a bag and it sits there on the floor or chair all by itself, guess what happens? It sets off alarms. The area is cleared and taped off, any flights that were supposed to depart there will have to wait, the bomb-sniffing dogs come and the police. Your left bag probably cost the airport a whole lot more than 247€. It happens all the time at the Meeting Point or the train stations. A total pain in the neck for your fellow travelers.

Lesson, cut your losses or pay.

Your choices are pay the shipping or go back and pick it up.

If going back to retrieve it is not feasible and the shipping costs are 2 -3 times the value of the goods, I see no problem in choosing what to do.

There is no magic discount shipping choice.