Hi,
With Falang, the translations are stored in the falang_content table in the database.
HikaShop bases itself on that information to store and load the translations of the elements in the backend, either in that table, or in the language override file of Joomla.
On the frontend, Falang uses a plugin to dynamically load the translations.
So, if you go in your PHPMyAdmin and rename the falang_content table, it will force HikaShop to use the language override file of Joomla to load and store the translations, and it will work on the frontend.
The downside, is that you'll have to redo your translations as there is no mechanism to migrate the translation data from Falang to the Joomla language override file.