Q. If the child is born (conceived by sperm left over after his fathers death – see previous question) will he be a Cohen as his father was? Will he have to say kadish on his yortzait?
A. Poiskim disagree on this matter Beiros Shlomo (P. 270 nts.) maintains that he is considered the father's child for everything (inheritance and incest marital prohibitions) excepting Yibum, since at the time of death he did not have any children, on the onset yibum could be permitted, however because of marais ayin, chalitza should be done.
However Mishp'tey Uziel (53) disagrees and maintains that even when the father is alive, a child born by artificial insemination is not related at all to the donor. (see Tashbatz 3: 263, Yabia Omer E.H. 1:5). There are other opinions that differentiate to what he is considered a child and what not (see Noam 1: p.155 and Nishmas Avrohom 3 p. 10)
Horav Shlomo Miller's Shlit"a opinion is that following the rule of most Poskim the child would be considered a Cohen and would recite kadish on his yortzait.
Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit"a
Important Numbers
