  It is shown in a quantum-mechanically exact manner that a supersymmetric and
$\kappa$-symmetric D-string action in a general type IIB supergravity
background is transformed to a form of the type IIB Green-Schwarz superstring
action with the SL(2,Z) covariant tension through an S-duality transformation.
This result precisely proves a conjecture mentioned previously that the SL(2,Z)
S-duality of a super D-string action in a flat background is also valid even in
a curved IIB background geometry. We point further out the validity of the more
generalized conjecture that various duality relations of super D-brane and
M-brane actions originally found in a flat background also hold true in general
ten dimensional type II supergravity and eleven dimensional supergravity
background geometries by applying the present formalism to those cases.
