Yes, angular momentum of a rotating body changes with radius.

What happens to angular momentum if radius increases?

Angular momentum is defined as L=r×p where r is the center of rotation and p is the momentum. Since angular momentum is conserved, if r decreases then p must increase.

What is the relation between angular momentum and radius?

Angular momentum is defined, mathematically, as L=Iω, or L=rxp. Which is the moment of inertia times the angular velocity, or the radius of the object crossed with the linear momentum. In a closed system, angular momentum is conserved in all directions after a collision.