When is a mourner allowed to get a haircut for the first time

A mourner in the year of mourning for his father, when is he allowed to cut the hair on his head for the first time?

In the Talmud, Moed Katan, page 22b, it is stated: "For all the deceased, one may cut hair after thirty days; for his father and mother, until his friends rebuke him." In Beit Yosef, it implies that immediately after the thirtieth day, one can be rebuked, and it is permitted to cut hair. In Darkei Moshe, s.k. 3, several customs are mentioned. In Shefer Terumat HaDeshen, Agudah, and Maharil, it is written that the custom is that the period for rebuke is three months. In Kol Bo, it is stated that the period is two months, and it is mentioned in the name of Maharil that in some places, the custom is not to cut hair for all twelve months, and it concludes that this is the custom in our country, and if the hair becomes too heavy, they are lenient, and there are those who are lenient, and no one protests since it is merely a stringency. In Shulchan Aruch, Siman 394, paragraph 4, it is written: "For all the deceased, one may shave after thirty days; for his father and mother, until his friends rebuke him." Rema writes: "The period for rebuke is disputed, and the custom is three months (according to the opinion of Mahari in his rulings, Agudah, Maharil, and Ran). In these places, the custom is not to cut hair for father and mother for all twelve months (Maharil, custom of some places), unless necessary, such as if the hair becomes too heavy, or if he walks among non-Jews and is disgraced among them due to his hair, then it is permitted to cut (so answered AZ)." In practice, in the custom brought by Rema, where it is customary to wait three months, it is written in Shu"t Igrot Moshe (Yoreh De'ah, part 3, Siman 156) that the period of three months is without rebuke, and there is no stringency not to rebuke him within three months. However, the custom is not to rebuke him for three months, and here are the words of Meiri (perhaps this is the source of the custom): "The custom of friends is not to rebuke until three months have passed, and if the time for rebuke has arrived and he sees his friends despairing of him, he is also allowed to cut, and this is what is said in the Jerusalem Talmud: until he grows his hair or until his friends rebuke him, and there are those who do not cut hair for all twelve months, but after three months, they are lenient in cutting." Further, the later authorities dispute from when to count the three months: Maharsham wrote that three months is from the last haircut. However, Maharam Shik, Yoreh De'ah, Siman 371, wrote that they count from the beginning of mourning, and the custom in this is to count three months from the last haircut. Some are stringent to count from the day of death. In Mishnah Berurah, Siman 548, s.k. 34, it is written: "And if they rebuked him even on the thirtieth day, it is permitted [AR]:" (and there are versions in Mishnah Berurah that it is within thirty days, and this is a scribal error), and therefore by law, this is sufficient, and although it is customary to wait three months, one may be lenient.