What is the ruling on a sister wearing trousers with a head covering, and is it correct to advise her to wear a skirt, given that her 'awrah would not be exposed when riding public transportation or ascending stairs?

The brother who asked the question should enjoin his sister to fear Allah. She must seek out the শরعي (Shari'i) dress that does not reveal the size of her limbs and is not transparent, showing her skin. It is not permissible for a woman to wear trousers.