My mother passed away and has some unfulfilled fast days. Can I fast on her behalf?

Any relative of the deceased may fast on behalf of a deceased person. A non-relative may also fast but only with the permission a relative.
The ruling
You may choose either to fast on behalf of your mother or feed a poor person for each of her unfulfilled missed fast-days. According to Shafi'i scholars, the kaffara [expiation] consists of one mudd of wheat, dates, or any of the staple food of the country. A mudd is half a kilo approximately. You may calculate the number of your mother’s missed fast-days and divide them among you and your siblings; each one is free to choose how to make them up. If you choose to feed the poor, there is no objection to giving out the value of the food in cash.

And God Almighty knows best.