  We continue to investigate the dual description of the Virasoro conformal
blocks arising in the framework of the classical limit of the AdS$_3$/CFT$_2$
correspondence. To give such an interpretation in previous studies, certain
restrictions were necessary. Our goal here is to consider more general
situation available through the worldline approximation to the dual AdS
gravity. Namely, we are interested in computing the spherical conformal blocks
without the previously imposed restrictions on the conformal dimensions of the
internal channels. The duality is realised as an equality of the so-called
heavy-light limit of the n-point conformal block and the action of n-2
particles propagating in some AdS-like background with either a conical
singularity or a BTZ black hole. We describe a procedure that allows relaxing
the constraint on the intermediate channels. To obtain an explicit expression
for the conformal block on the CFT side, we use a recently proposed recursion
procedure and find full agreement between the results of the boundary and bulk
computations.
