If he fulfils his vow, is it permissible for him to eat from it?

The basic principle
concerning vows is that if what is vowed is something that is permitted in
Islam, it should be given in the manner specified by the one who made the
vow. If he did not specify anything then it is a kind of charity and may
be given in any way in which charity is given, such as to the poor and
needy. 

With regard to eating from it, if the custom in the country
where he lives is for the one who makes a vow of giving something edible to
eat from it, it is permissible for him to do so, based on the local
traditions and customs. Similarly, if he intended when he made the vow to
eat from it, then both custom and intention apply to the part that he eats,
and that is not part of that concerning which the vow was made. A fatwa was
issued by the Standing Committee concerning that, which states the
following: 

The way in which a vow is
to be fulfilled is to give in the manner intended by the one who made the
vow, within the limits of sharee’ah. So if he intended the meat mentioned in
his vow to be given to the poor, it is not permissible for him to eat from
it, but if he intended in his vow to give it to his family or to a group of
whom he is a member, then it is permissible for him to eat as one of them,
because the Prophet (peace and blessings of Allaah be upon him) said:
“Actions are but by intentions and each person will have but that which he
intended.” The same applies if he stipulates that in his vow or if that is
the custom in his country. 

From Fataawa al-Lajnah al-Daa’imah li’l-Ifta, 23/390 

And it says in Fataawa al-Lajnah al-Daa’imah (23/392):
Whoever makes a vow to offer food, the basic principle is that the one who
makes the vow should not eat from it unless he has stipulated or intended to
eat from it, in which case it is permitted for him to eat as he stipulated
or intended. 

And Allaah knows best.