Mo. Rev. Stat. § 441.130: Alienee or assignee may recover rent.

If the owner or holder of the lands, tenements, an estate or a lease term alienates or assigns such owner's or holder's lands, tenement, estate or term, or the rent thereafter to fall due on such premises after such alienation or assignment, the owner's or holder's alienee or assignee may recover such rent paid to such owner or holder after such alienation or assignment.