Spell checking in Falkon currently supports only basic functionality and also needs a custom format of dictionaries. This is a limitation that comes with QtWebEngine. Dictionaries needs to be in a special format that uses Chromium, with the extension .bdic. QtWebEngine comes with an utility to convert Hunspell dictionaries (.dic) to this format.
qwebengine_convert_dict /path/to/hunspell/dict.dic /output/path/to/created.bdic
Created .bdic dictionaries then need to be moved to one of the directories shown in the Preferences.
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