My brother died a year ago, what should we do with his shoes?

There are differing opinions about this. It is recommended to conduct yourselves in accordance with the common custom which is neither to wear the shoes nor to give them to the poor. This custom refers to shoes that the deceased wore while passing or during his illness. They should be thrown away or sold to a gentile who is buying them for himself, in order to avoid causing danger to any Jew. The money should be given to the poor in merit of the deceased. (ספר חסידים סימן תנד, כף החיים יו"ד סימן קטז אות קמא, אגרות משה יו"ד ג סימן קלג, שו"ת יביע אומר ח"ג יו"ד סימן ה, וע"ע באריכות בספר שמירת הגוף והנפש חלק א סימן עא).