Ruling on the wudoo’ ofone who washes his arms from the wrists to the elbows, and does not wash the hands

In my community and in the Muslim world, many Muslims make the mistake
of only washing from the wrist to the elbows in elbows instead of
washing the hands also in wuduu. Although I try to tell people,
sometimes we are led by different people in prayer(we do not have an
imam). So if I do not know if this person does wuduu correctly or not,
should I pray behind him anyway? Does it depend on how much doubt I
have? Someitmes I may already know the brother who is going to lead us
and I have a big feeling he does wuduu in hte worng way yet should I
ask him as he is about lead prayer.
Praise be to Allaah.
Firstly:
The parts of the body that must be washed in wudoo' are mentioned in
the verse in which Allah, may He be exalted,says (interpretation of
the meaning): "O you who believe! When you intend to offer As-Salat
(the prayer), wash your faces and your hands (forearms) up to the
elbows, rub (by passing wet hands over) your heads, and (wash) your
feet up to ankles" [al-Maa'idah 5:6].
Allah, may He be exalted,has made it obligatory to wash the arms up to
the elbows after washing the face, and this cannot be done except by
washing the arms from the fingers upto the elbows. The one who limits
it to washing them from the wrists to the elbows has not performed
this obligation.
With regard to washing their hands at the beginning of wudoo', this is
Sunnah, and cannot suffice for the obligatory action, according to the
majority of scholars, contrary to the Hanafi view.
The majority of scholars are of the opinion that itis obligatory to
wash theparts of the body in wudoo' in the correct order as mentioned
in the verse: washing the face, then washing the arms, then wiping
over the head, then washing the feet.
Based on that, it is not valid to regard washing the hands at the
beginning of wudoo' as being sufficient and not washing them again
with the rest of the of the arm, because that leads to failure to
follow the proper sequence, washing of the face in the middle of
washing the arms. What is required is to wash the entire arm, after
washing the face.
To sum up: if a person does wudoo' and washes his hands, then rinses
his mouth and nose, and washes his face, then he washes his arms from
the wrists to the elbows, his wudoo' is not valid according to most of
the scholars.
Shaykh Ibn Jibreen (may Allah preserve him) was asked: What is the
rulingon one who washes his arms from the wrist to the elbow, without
washing his hands, thinking that his washing of his hands at the
beginning of wudoo' is sufficient? Does he have to repeat wudoo'?
He replied: It is not permissible when doing wudoo' to wash the
forearm only, without the hand. Rather when he has finished washing
his face, he should start to wash the arms, and he should wash each of
them from the fingertipsup to the elbow, even if he washed his hands
before his face, because washing them the first time is Sunnah, and
washing them after the face is obligatory. If a person only washes his
arms from the wrist to the elbow, then he has not completed wudoo' as
required, and he has to repeat his wudoo' after completing it, or
hehas to wash what he omitted if only a short time has passed (since
he completed it), so he should wash the hands and what comes after
that.
End quote from al-Lu'lu' al-Makeen min Fataawa Shaykh Ibn Jibreen, p. 77
Shaykh Ibn 'Uthaymeen (may Allah have mercy on him) said: Here we
should point out something that many people neglect, as they wash the
arm from the wrist to the elbow, thinking that they had finished
washing the hands before washing the face, but this is not correct. It
is essential to wash the arm from the fingertips to the elbows.
End quote from al-Liqa' ash-Shahri, 3/330
And Allah knows best.