I’ve found a solution a few minutes after posting this question.
In case anyone is also looking for that:
1. create wp-content/languages/plugins/ directory
2. copy selected ACF translation file (.po and .mo) from ACF plugin lang/ folder to created wp-content/languages/plugins/
3. customize the translation with e.g. Poedit or any other program for editing .po files and then generate .mo
This way your translation will be preserved even after plugin update.
