Is a Muslim husband obliged to give zakat al-fitr on behalf of his Christian wife?

In the answer to question no.
99353 we stated that there is a difference of
scholarly opinion as to whether a husband is obliged to give zakat al-fitr
on behalf of his Muslim wife. 

But if the wife is one of the People of
the Book (Christian or Jewish) the husband is not obliged to give zakat al-fitr
on her behalf, because zakat al-fitr is only obligatory for Muslims. 

This is indicated by the report narrated
by Ibn ‘Umar (may Allah be pleased with him) who said: The Messenger of
Allah (blessings and peace of Allah be upon him) enjoined zakaat al-fitr, a
saa‘ of dates or a saa‘ of barley, on behalf of free and slave, male and
female, young and old, among the Muslims.

Narrated by al-Bukhaari (1503), Muslim
(984). 

The words “among the Muslims” indicate
that being a Muslim is a condition of zakat al-fitr being obligatory, and
that it is not required of the disbeliever on his own behalf. There is
scholarly consensus on this point.

End quote from Subul as-Salaam (1/538) 

In Mughni al-Muhtaaj (2/112) it
says: No zakat al-fitr is required of a disbeliever, because the Prophet
(blessings and peace of Allah be upon him) said:  “… among the Muslims”.
This is consensus, as al-Maawridi said, because it is a means of
purification and that does not include the disbeliever. End quote. 

Al-Haafiz said in Fath al-Baari
(3/369): 

The words “male and female” clearly
indicate that it is obligatory for all women, whether they have husbands or
not. … Then he said: (The scholars) are agreed that a Muslim should not give
it on behalf of his non-Muslim wife. End quote.