bequeath
To leave something to someone after you die.
To bequeath means to leave something to someone after you die, usually through instructions in a legal document called a will. When a grandmother bequeaths her antique pocket watch to her grandson, she's making sure he'll receive it after she passes away. When a wealthy inventor bequeaths money to build a library, he's arranging for that gift to happen after his death.
People bequeath all sorts of things: family heirlooms, money, land, or even collections of books or art. Benjamin Franklin famously bequeathed money to the cities of Boston and Philadelphia with instructions that it couldn't be touched for 200 years, turning thousands of dollars into millions.
You can also use bequeath more broadly to describe passing down anything valuable to future generations, not just through a will. A teacher might bequeath knowledge and wisdom to students. A retiring coach might bequeath a winning tradition to the team. In this sense, what you bequeath doesn't have to be an object at all. It can be ideas, values, or ways of doing things that you pass along for others to treasure and use.