Thank you for this explanation!
I had been racking my brains for months on why the first article vanishes, and I had come to the same conclusion, but without any clear evidence of this in Duolingo's notes.
The 'Countries' unit does show the loss of the article in expressions such as 'the Welsh flag → baner Cymru, but a general rule in terms of "the (noun 1) of the (noun 2)" turns into "(noun 1) of the (noun 2)" is not explicitly mentioned (or maybe I hadn't understood it this way).
If you want a historical explanation, that may help you get it right, the literal translation of swyddfa'r heddlu is the police's station. It's just that Welsh has no 's and the word order is different, but you now have exactly the same in both languages, with the article before 'police'.