Chouby on "[Plugin: Polylang] Text configured by theme's settings not translated - how to do this?"

Yes and you should close with </key> below. Somethig like this:

<wpml-config>
	<admin-texts>
		<key name='theme_option_name'>
			<key name="header-info_title" />
			<key name="header_info_slogan" />
			<key name="header_info_button_txt_1" />
			<key name="header_info_button_txt_2" />
		</key>
	</admin-texts>
</wpml-config>