Which is better: for the questioner to perform Hajj on behalf of his deceased parents, or to donate the cost of Hajj for the construction of a mosque and Islamic center in a Western city, knowing that the father did not fulfill the pillars of Islam and the mother was committed to prayer and fasting? And is it permissible to donate or perform Hajj on behalf of a father who did not pray or fast?

Your father — may Allah forgive him — was extravagant, but Allah's mercy encompasses all things. If he died upon monotheism, then it is hoped that Allah's forgiveness will include him. You must honor him and pray for him. There is no blame upon you if you perform Hajj on his behalf or appoint someone to do so.

If Hajj became obligatory upon one or both of your parents and they did not perform it before they died, then Hajj must be performed on their behalf from their estate. The cost for their Hajj should be disbursed before the division of the inheritance.

If Hajj became obligatory upon them, but they did not leave behind enough to perform Hajj on their behalf, then it is better for you to perform Hajj on their behalf or appoint someone to do so, in order to absolve them. This is recommended for the heir, even if the deceased did not make a will concerning it, as it lifts the obligation from the deceased.

However, if Hajj was not obligatory upon them and you wish to perform it as a voluntary act on their behalf, there is no blame upon you, provided you have already performed Hajj for yourself.

Perhaps performing Hajj on their behalf or appointing someone to do so is more preferable than contributing to the construction of a mosque, given that this Hajj is an obligation on their behalf, even if it wasn't obligatory upon them.