Is it permissible to continue giving Zakat to a poor, sick friend, noting that he owns luxuries in his home?

Obligatory charity (zakat) is not due on a monthly salary except under certain conditions, and if it becomes due, it must only be given to its rightful recipients. If zakat is paid to its rightful recipient, the payer is absolved of the obligation, even if the poor person uses it for non-essentials. As for voluntary charity (sadaqat al-tatawwu'), it is preferable to give it to those in need. However, if it is given to someone who is not eligible, such as a wealthy person, the giver will still be rewarded for it. The proof for this is the hadith of Abu Hurayrah (may Allah be pleased with him) that a man gave charity to a prostitute, a rich man, and a thief, and his charity was accepted. He was told: "As for the prostitute, perhaps she will refrain from her immorality because of it. And perhaps the rich man will take heed and spend from what Allah has given him. And perhaps the thief will refrain from his stealing because of it." So, if the person you give charity to is poor, they are a recipient of charity in all cases. If they are wealthy, it is not permissible to give them obligatory zakat, but it is permissible to give them voluntary charity, although this is not the most preferable option.