She made a bequest of some money as a contribution to building a mosque; can the executor of the bequest give it to the poor because they are in need?

Praise
be to Allah.

Firstly: 

Building mosques, maintaining them and preparing them for the
worshippers is one of the best of good and righteous deeds for which Allah
has decreed an immense reward. It comes under the heading of ongoing charity
(sadaqah jaariyah) which will continue to bring reward even after a person’s
death. Allah, may He be exalted, says (interpretation of the meaning):

“The Mosques
of Allah shall be maintained only by those who believe in Allah and the Last
Day; perform As-Salat (Iqamat-as-Salat), and give Zakat and fear none but
Allah. It is they who are expected to be on true guidance”

[at-Tawbah 9:18]. 

The Prophet (blessings and peace of Allah be upon him) said:
“Whoever builds a mosque, Allah will build for him a house in Paradise.”
Narrated by al-Bukhaari (450) and Muslim (533), from the hadith of ‘Uthmaan
(may Allah be pleased with him). 

For more information, please see the answer to question no.
146564

Secondly: 

The basic principle is that it is obligatory to carry out the
wishes of the one who left that endowment (waqf), and it was narrated that
there was scholarly consensus on this point in general terms. 

Al-Hajjaawi (may Allah have mercy on him) said in Zaad al-Mustaqni‘:
It is obligatory to carry out the wishes of the one who made the endowment. 

Shaykh Muhammad al-Mukhtaar ash-Shanqeeti (may Allah preserve
him) said: That is, it is obligatory upon the one who has been appointed to
look after the endowment to act in accordance with the wishes stipulated by
the one who made that endowment. 

If the one who made the endowment stipulated conditions, or
it set out specific signs or characteristics to determine who is entitled to
benefit from his endowment, then it is obligatory to act accordingly, and it
is not permissible to ignore these conditions or tamper with them. That is
according to the consensus of the scholars, may Allah have mercy on them.
When ‘Umar ibn al-Khattaab (may Allah be pleased with him) wrote his will,
in which he left his land in Khaybar as an endowment (waqf), he entrusted
supervision of it to the Mother of the Believers Hafsah (may Allah be
pleased with her), then after her to the most mature and just of his
descendants, and he stipulated conditions on how the income from the
endowment was to be spent and used. The practice among the leading scholars
and judges of the Muslims has been that the wishes of the one who left the
endowment should be followed and it is not permissible to cancel them, alter
them, change them or distort them. 

Hence the author said “it is obligatory”, which indicates
that the one who goes against that is sinning. Hence it is not permissible
to alter these instructions, unless the qaadi determines otherwise in
exceptional circumstances, which we will explain below, in sha Allah.
However the basic principle remains that it is obligatory to act in
accordance with these instructions and carry them out, and the conditions
may vary. If a person leaves a piece of land or anything else as an
endowment, he may stipulate that it is to be cared for by a particular
individual, or he may stipulate a particular beneficiary for the endowment,
or he may stipulate that this beneficiary should have certain
characteristics.

End quote from Sharh az-Zaad. 

To sum up: 

It is not permissible to transfer the endowment to someone
else, or to change the instructions of the one who made the endowment,
unless it is no longer possible to carry out the terms of the endowment as
stipulated. 

Please see also the answer to question no.
140176 

Based on that, what you must do is act in accordance with
your grandmother’s wishes, in compliance with the shar‘i texts to that
effect, as mentioned above. Even those scholars who say that it is
permissible to change the endowment or change its conditions meant that that
applies only if it is better for the endowment and will enable people to
benefit from it more completely, and there is no interest to be served by
changing or annulling the endowment. 

And Allah knows best.