As the module does not support localization by itself, you can use the following procedure to "simulate" a localized module.

Drop two instances on the module in the page

Use DSLocalizator to make 1st module to hide when the 1st lenguage is selected and make the 2nd module to hide when 2nd language is selected.

Now, when you enter the page, you will see only one module. Changes made when 1st localization will be only there when 1st language is selected and the same for the second language

Hope it helps