Q. If someone has yohrtzait on Shiva Asar Betamuz, but because of illness is not fasting a full day, can he be called to the Torah o this year when the taanis falls on a Thursday and the Torah would have been read anyway?
A. Mishna Berura (566: 19) quotes Magen Avrohom that the ruling of the Shulchan Aruch not to give an aliyah to someone not fasting applies only during Mincha but not during Shacharis in the days when there would be otherwise also Kerias Hatorah such as Mondays and Thursdays. Mishna Berura quotes other Poskim that debate the issue, and summarizes, that is he was called to an aliyah according to everyone he should proceed.
Although. it isn’t clear from his words if he can be called lechatchila to the Torah, Aruch Hashulchan (ibid.), Divrei Shalom (93) and others rule like the Magen Avrohom and Eliahu Rabbah that he can be called on the onset.
Horav Shlomo Miller’s Shlt’a opinion is similar.
Rabbi A. Bartfeld as advised by Horav Shlomo Miller and Horav Aharon Miller Shlit’a