Hi @jpjpb,
Facebook usually works on a 1-1 site/store ratio – that said you can link your Catalog Manger to different stores with the same account, it involves setting it up on Facebook’s side to understand this – WooCommerce’s side will ‘see’ the different sites connected to the Facebook account when running your connection the first time, and you should be able to choose them separately.
Be sure to connect the right store to the right Manager on the Business Manager/Catalog Manager on Facebook’s side, and also understand that it is very possible for the sync to mess up and stop working as Facebook / WooCommerce has not been fully tested outside of a 1-1 site/store ratio.