i see her really admiring the english monarchy in general and the strength that their monarchy has maintained under the rule of a female. i'm thinking she's studied the queen in depth as a strong example of a female who successfully led a country. additionally she probably respects the requirement of military service etc. she's a very proud liechtensteiner but part of her was pretty smiley when the UN called them out for inequality of genders when it came to ruling the country. she admires the people like him and tiane who can have their fun and rebound successfully from it and that's what she's looking to accomplish.
they probably would have done charity work together and such and bonded over being there because they want to be and want to do good not just because it looks nice for their people.