Pope John XXIII
Vital Football Legend
It used to be common but thankfully less so now with the big countries.I'm not recommending her.
She's at the top of her game and will continue to have great success there, I'm sure. Unless she has a particular passion for smashing glass ceilings, I doubt she has any desire to switch to the men's game herself.
It'd be like a man coaching women - unthinkable.
Shift someone like Klopp over to coach the women and it would be pointless. He wouldn't know the leagues, the players, the opponents, the tactics, the bits of coaching to focus on.
You can learn. But international football, where every competitive game matters is probably not the place