I actually found some answers, and passed them on the questioner. I am
posting them below, in case it is helpful to anyone else, or some of
our respected mashayikh want to add anything:

I took out my copy of Sh `Abdullah's booklet (Ta3reef Ahl al-Islam
bi-anna Naql al-`uDw Haram) after many years, and extracted
the following from it:

1) at the end of the mongraph, its date is given as 3 Dhul-Qa`dah 1407 H.
2) at the beginning, the shaykh mentions that 4 yrs earlier (i.e.
1403) while he was in Egypt, some medical students from Alexandria's
College of Medicine asked him some questions about the shar`i verdict
on some medical issues, which he answered and published as "Ajwibah
Hammah fi al-Tibb." One of these questions was about organ
transplantation, and it is this one of course that is the subject of
this monograph (Ta3reef Ahl al-Islam).
3) The shaykh if course opposed organ transplantation. He mentions
that after he had given this response (to the students), he saw in the
magazine al-Liwa' al-Islami, Issue 226, an article by Sh Sha`rawi
entitled, "al-Insan laa yamlik jasadhu fa-kayfa yatabarra3u
bi-ajza'ihi aw yabee3uha". This article agreed with Sh `Abdullah's
view, and gave extensive reasoning / evidences (istidlal).
4) He also refutes an article al-Muslimun magazine, 4 Shawwal 1407 /
30 May 1987, which contained a fatwa permitting organ transplant

5) It appears the shaykh maintained his view even later. (He died
around the early 1990s; sorry, don't remember exact year.)
My shaykh, Abu Idrees (mujaaz of Sh `Abdullah), wrote the following
response to me yesterday:
"I personally sent to Sh Ghumari the following question: Someone's
mother is about to die because she needs a kidney. Can one donate his
own kidney to save his mother life? (I purposefully made the question
to be very extreme). His answer was: No it is not allowed. He
responded to me when we were studying in the US (early nineties). He
also said that the Doctor is only a means to cure not the cure itself.

I wish I could pull out the letter where he had written the answer. I
recall we sent him a fax, and either himself or Mohammad Ali wrote the
answer by hand on it and faxed back. But it may take a while to find
the letter again.

I know the Sheikh has explained his evidences in one of his fatawa
books, and this how we sent him the question at that time.

If you need more detailed fiqh information you can check the following
valuable book (Syrian author is an authority on medical fiqh issues
because he is both a Doctor and a Faqih)

الموقف
الفقهي و
الأخلاقي من
قضية زرع
الأعضاء/
تأليف محمد
علي البار. - ط.1. -
دمشق، سوريا :
دار القلم، 199"
[end of quote from Sh Abu Idrees]

Was-salam
-sl