Hi @kassilukraine
The way you can use Smart Slider on multilingual sites is that you need to create a separate slider for each language:
https://smartslider.helpscoutdocs.com/article/1968-smart-slider-3-on-multilanguage-sites
Then at each slider you need to have the content on the language where you want to show the slider. So in a slider that appears for the English visitors, you need to have English text in the slider. If you have e.g. German as your second language then you need another slider displaying the content in German language.
So if you have a dynamic slider for your main language make sure it’s only published for the main language visitors. Then you’ll need to create a (separate) dynamic slider for the secondary language and publish that slider for the secondary language.
The [smartslider3 slider=3 lang=en_US]
shortcode is not for translation, but for displaying the slider on the given language only. Like in this case if you have an English and German site then this shortcode would make the slider appear only on the English site (with the content you set at the backend) but won’t display it on the other language site.