Mother's Ex Is Trying To Shake Her Down For Money

My mom broke up with her boyfriend and he bought tools for her home that he used while he was living with her. She did not ask him to buy them, he did it on his own. Now that he's leaving he wants her to pay for the tools. She has told him to take them since they're his, but he is refusing since he "won't have a use for them" at his place. Does she owe him this money? It's about $600.