Problem:
The stock is not in sync between original products and translations in WooCommerce.
Solution:
Check WooCommerce > WooCommerce Multilingual & Multi-Currency > Status.
It is very likely the case, that on top of this string, you will find a configuration warning related to custom fields, like for example the field "_stock".
You will need to go to WPML > Settings > Custom Field Translation and click "Show system fields", then adjust the settings accordingly, in order to have not any config issues longer show up on the screen mentioned above.
The "_stock" field for example always should be set to "Not translate".
Other fields should always be set to "Copy", like:
total_sales
_backorders
_downloadable
_download_expiry
_download_limit
_manage_stock
_regular_price
_sku
_sold_individually
_stock_status
_tax_class
_tax_status
_virtual
Take note that WPML does block those settings by default and they should not be altered by a user, but it may occur that specific WooCommerce Addons alter those settings.
Relevant Documentation:
https://wpml.org/documentation/getting-started-guide/translating-custom-fields/
