Can I give charity on behalf of someone who died?

The Prophet said yes

A man told the Prophet Muhammad ﷺ that his mother had died suddenly and that he thought she would have given charity if she could have spoken. He asked if she would be rewarded if he gave charity on her behalf, and the Prophet said yes (Sahih al-Bukhari 1388). In another report, the Companion Sa'd ibn Ubadah asked the same about his mother, and when the Prophet said it would benefit her, Sa'd gave his garden as charity in her name (Sahih al-Bukhari 2756).

Good ways to do it

• Ongoing charity: a water well, a share in a school or mosque, Quran copies. See What is sadaqah jariyah?
• Feeding people: meals for the poor in their name.
• Regular giving: a small monthly donation in their memory.
• Paying their debts: settling what they owed is one of the most important things you can do for a deceased person.

Simply make the intention that the reward goes to them. Many charities also let you add a name to the donation.

Non-Muslim relatives

This is a tender subject for many converts. Most scholars say the reward of charity given on behalf of someone who died as a non-Muslim doesn't benefit them in the hereafter, since that depends on faith. But Islam doesn't ask you to forget or stop honoring them:

• You can give charity in their memory, with the reward for yourself, as a way of continuing the kindness they showed.
• You can do good deeds they would have loved, like supporting a cause they cared about.
• Allah alone judges every soul, with perfect justice and mercy.

See Can I inherit from my non-Muslim parents as a Muslim?

Other gifts to the deceased

Besides charity, scholars agree that a deceased Muslim benefits from du'a, from having their debts paid, and from Hajj or fasting done on their behalf in certain cases. The hadith of the three deeds that continue after death includes a righteous child who prays for them (Sahih Muslim 1631).