lay claim to (something)
To assert that one has the legal or proper right to own or possess something. If no one lays claim to the wallet within 48 hours, you'll be able to keep it for yourself. The youngest son is laying claim to the business now that their father has passed away.
lay ˈclaim to something
state that you have a right to something: ‘The Lamb and Flag’ lays claim to being the oldest pub in London.