I guess you’ll have as many answers as there are airlines in the Alliance!!!
Personally I’d go with Miles and More, After 2, maybe 3, trips she’ll be silver, which then will give 25% more base miles. From FRA she can fly to London as well as most regional airports.
Of course if flying round the region then indeed give Thai and perhaps SQ a thought.
Air New Zealand also fly’s direct HK to LHR, so also worth considering if London is where she needs to be.