"Matěj proposed to her two months ago."
Translation:Matěj ji požádal o ruku před dvěma měsíci.
That sounds like the 19th century to me. I even found a related example: "...,který také požádal ji o ruku." (Hurban, 1877). Sounds weird today.
With JI after POŽÁDAL?
If you kicked Matěj out, you can do it "Požádal ji o ruku" (he proposed to her), I guess we know who he is from context.
But once you put Matěj in or ON in, you cannot swap it around like that. So no !Matěj požádal ji o ruku"