Praise be to Allah.
The father has rights over his son, even if he behaves badly, does wrong or persists in sin, because his right to kind treatment and obedience in that which is right and proper is guaranteed according to the Islamic texts. If Allah, may He be exalted, has affirmed the rights of a mushrik father – and even one who calls his children to ascribe partners to their Lord, may He be glorified and exalted – to respect and kind treatment, then a father whose wrongdoing is less serious than that is even more entitled to that respect and kind treatment. Allah, may He be exalted, says (interpretation of the meaning): “But if they (both) strive with you to make you join in worship with Me others that of which you have no knowledge, then obey them not, but behave with them in the world kindly, and follow the path of him who turns to Me in repentance and in obedience. Then to Me will be your return, and I shall tell you what you used to do” [Luqmaan 31:15].
Hence it is known that no matter how kindly your mother’s husband treated you and how many favours he did for you, your father’s rights over you are greater. If you fell short in upholding your father’s rights when he was still alive, then you must ask Allah for forgiveness for that, and offer a great deal of supplication for him for mercy and forgiveness, and give charity on his behalf, according to your means, for these are ways of honouring him after his death. The scholars of the Standing Committee for Issuing Fatwas said: The Sunnah indicates that it is prescribed to honour parents after they die, by offering supplication for them, carrying out their last wishes, upholding ties of kinship that you would not have except through them, and honouring their friends.
End quote from Fataawa al-Lajnah ad-Daa’imah (25/182
Shaykh Ibn Baaz (may Allah have mercy on him) said: Part of honouring one’s parents is giving charity on their behalf, offering supplication for them, and doing Hajj and ‘umrah on their behalf.
End quote from Majmoo‘ Fataawa Ibn Baaz (8/344)
With regard to calling your mother’s husband “father”, there is nothing wrong with that if it is by way of honouring and showing respect, not by way of attributing yourself to him. We have discussed this with evidence and in detail in fatwa no. 100329
With regard to giving charity on behalf of your mother’s husband – after his death – and doing Hajj on his behalf, this is permissible and indeed is recommended, because it comes under the heading of returning favours and acknowledging kindness. The scholars stated that the deceased may benefit from charity given on his behalf. It says in Tuhfat al-Muhtaaj (7/72): The deceased may benefit from charity given on his behalf, which includes donating a Mushaf and the like as a waqf, digging a well, or planting a tree during his lifetime or after his death. End quote.
The scholars also stated that the deceased may benefit from Hajj done on his behalf. Shaykh Ibn Baaz (may Allah have mercy on him) said: Hajj on behalf of the deceased, or ‘umrah on behalf of the deceased, is one of the best acts of worship. The Muslim deceased may benefit a great deal from it. The Prophet (blessings and peace of Allah be upon him) was asked about that many times, and he said to the questioners, both male and female: “Do Hajj on behalf of your father” and “Do Hajj on behalf of your mother.” Someone else said to him: I have entered ihram on behalf of Shubrumah. He said: “Who is Shubrumah?” He said: A brother of mine – or a relative of mine. He said: “Do Hajj on your own behalf (first), then do Hajj on behalf of Shubrumah.” People fall into different categories. Some of them did the obligatory Hajj and the obligatory ‘umrah (when they were alive); in this case if Hajj is done on such a person’s behalf, then it is naafil (supererogatory), and if ‘umrah is done on his behalf, it is naafil. If his brother or father or relative or one of his brothers in Islam does Hajj on his behalf, all of that is good, and the same applies to ‘umrah. If he had not done Hajj or ‘Umrah, then the one who does Hajj on his behalf has done the obligatory Hajj on his behalf, and likewise the one who does ‘umrah on his behalf has done the obligatory ‘umrah. In all cases, he will be rewarded and the deceased will be rewarded; both of them will be rewarded – the one who does it will be rewarded for his good deed and kindness towards his brother, and the deceased will also be rewarded for that. The same applies to giving charity, and to offering supplication. If he gives charity on his brother’s behalf, both he and the deceased will be rewarded, and if he prays for his deceased brother, he will be rewarded and the deceased will benefit from the supplication.
End quote from the shaykh’s website on the following link:
It should be noted that if a person wants to do Hajj on behalf of someone else, he must first have done Hajj on his own behalf, as we have explained in fatwa no. 1463
Finally, we should point out that your honouring your father and your parents in general, whether that is during their lifetime or after their death, by offering supplication for them, giving charity on their behalf, and so on, brings greater reward than your kindness to your mother’s husband or anyone else..
And Allah knows best.