The Sunnah is the put the hair of a deceased woman into three braids. It was narrated that Umm ‘Atiyyah (may Allah be pleased with her) said: One of the daughters of the Prophet (blessings and peace of Allah be upon him) died. The Prophet (blessings and peace of Allah be upon him) came to us and said: “Wash her with lotus leaves an odd number of times, three, or five, or more than that if you see fit, and put camphor in (the water) the last time, or a little camphor. And when you have finished, let me know.” When we had finished, we let him know, and he gave us his waist wrapper (to shroud her in). And we put her hair into three braids and put them behind her.
Narrated by al-Bukhaari, 1263; Muslim, 939
According to a report narrated by Muslim (939): And we put her hair in three braids, two at the sides and one at the front.
Badr ad-Deen al-‘Ayni (may Allah have mercy on him) said: What is meant by “we put her hair in three braids” is one braid at the front of the head and two braids at the side of the head. Our explanation is indicated by the report narrated by Muslim: “And we put her hair in three braids, two at the sides and one at the front.”
End quote from Sharh Sunan Abi Dawood, 6/74
With regard to braiding the hair of a deceased man, it is not mustahabb because it is not proven. Many people died at the time of the Prophet (blessings and peace of Allah be upon him) and there is no report to suggest that the hair of any one of them was put in braids. This is indicated by the texts of the fuqaha’; they clearly state that this is mustahabb in the case of women, but not men.
Al-Bukhaari (may Allah have mercy on him) included a chapter in his Saheeh entitled: Chapter: (Braiding) the woman’s hair in three braids.
Ash-Shaafa‘i (may Allah have mercy on him) said: The woman is like a man in terms of her ghusl, but there are some additional requirements in the case of the woman, and her hair is to be put in three braids, two of which should be placed behind her.
End quote from al-Umm, 8/131
Al-Bahooti (may Allah have mercy on him) said:
And it is makrooh to comb the hair of the deceased, whether on his head or his beard, because that will pull it unnecessarily. It was narrated from ‘Aa’ishah that she passed by some people who were combing the hair of a dead man, and she told them not to do that and said: Why are you combing the hair of your deceased? But it is Sunnah to put the hair of a female into three braids and let them hang behind her.
End quote from Daqaa’iq Ooli an-Nuha, 1/350
To sum up:
Braiding the hair is only mentioned with regard to washing the woman, not the man.
With regard to parting a man’s hair from the middle when doing the ghusl, as mentioned in the question, there is no basis for this in the Sunnah as far as we know. The case of the deceased is different from the case of one who is alive; because of that the majority of scholars are of the view that it is makrooh to comb the hair of the deceased, as quoted above from the Hanbalis.
Those who disagreed with the majority, namely the Shaafa‘is, only said that that is permissible if the hair is stuck together for some reason; this does not mean that it is Sunnah. And they stipulated that it should be done with a wide-toothed comb, so that it does not pull out the hair of the deceased.
End quote. Ahkaam fi’l-Fiqh al-Islami by Taha Muhammad Faaris, 235-257
And Allah knows best.