I have to apologize and I'm mortified for having created you problems, but upon further reasoning I realized that making this purchase would be really really bad for me...
The reason I requested this item was because Nintendo stop selling this in Europe (and recently in USA too).
I'm not much familiar with selling, so when I requested if it was possible to add this item, it didn't even crossed my mind that the price for it would be raised x_x
To make things worst, I just recently learned (after making the request) that ion-battery lifespan degrade over time even when not used, I was purchasing it with the idea of future-proofing and be able to play again with my 3ds in 1 or 2 years, but by that time, the battery might very well be dead.
So with the price of the battery, the delivery, Italy's Custom and the fact the battery keep degrading when not used, if I where to purchase I would be putting myself in a situation of having spent a total of 6000yen or more for something that doesn't work when I'll decide to use it.
I'm mortified for having created you problem and for not having realized all of this sooner, I'm telling you know so that you have a chance to replace it from the place you bought it, with an item that is more easy to sell on your store. My apologize