His half-sister from his father has a half-sister from her mother. Is it permissible for him to marry her?

Yes, that is permissible. 

Shaykh Saalih al-Fawzaan said: 

If you have a half-sister
from your father, then it is permissible for you to marry her half-sister
from her mother, because there is no relationship between you and her
half-sister from her mother that would prevent that. Allaah says
(interpretation of the meaning):  

“All others are lawful”

[al-Nisa’ 4:24]

al-Muntaqa, 5/258. 

Shaykh al-Islam Ibn
Taymiyah (may Allaah have mercy on him) narrated that the Muslims were
unanimously agreed that this kind of marriage is permissible. He said: It is
permissible for a man’s half-sister from his mother to marry his
half-brother from his father. This is unanimously agreed upon among the
Muslims and there is no dispute concerning that. And Allaah knows best. 

From al-Fataawa al-Kubra, 3/163.