All property, real or personal, belonging to any of the cities or towns prior to consolidation, unless the agreement for consolidation otherwise provides, immediately upon the accomplishment of consolidation, shall vest in and become the property of the consolidated city or town. All indebtedness, claims, demands, or rights owing or belonging to any of said cities or towns prior to consolidation in like manner shall vest in and become due to the consolidated city or town, which shall thereafter have the right to demand, have, sue for, recover, and enforce the same in its own name.