Issue with WooCommerce Product permalinks

Hi,

I’m using WooCommerce on a Multisite installation.
I have different permalinks for different languages, setting Product permalink base:
EN – /product/%product_cat% ? mydomain.com/product/product-category/product-name
IT – /prodotto/%product_cat% ? mydomain.com/prodotto/categoria-prodotto/nome-prodotto

When I switch from Italian product to English product it works like for other type of content (posts, pages, …), but from English to Italian I get a wrong permalink:
IT – mydomain.com/product/categoria-prodotto/nome-prodotto
So I get a 404.
Is it possible to fix it?

Thanks
Davide

https://www.ads-software.com/plugins/multisite-language-switcher/