Is it permissible for a girl to greet a stranger with salam?

Is it permissible for a girl to greet a stranger with salam?

Ibn Hajar al Haytami in his book «Tuhfat alMuhtaj» writes, “It is desirable (sunna) for a woman to greet another woman with salam, her mahram (brother, father, grandfather, niece, etc.), her master (if she is a slave) and her husband. Also for an old woman for whom men do not experience attraction it is desirable to greet a strange man. In all these cases (i.e., when a stranger greets her with salam, etc.) she (the old woman) is obliged to respond to their salam.”

“As for a girl to whom men are attracted, she is forbidden (haram) to respond to the greeting of a stranger, if there is no other woman (or man) with her. She is also forbidden to greet a stranger first.”

“For a man it is undesirable (karahat) to respond to the salam of a strange woman and also to greet her.”

“If a man greets two or more strange women, one of them must respond to his greeting.”

Source: Tuhfat al Muhtaj, vol. 9, p. 224