  We complete the nonlocal-in-time effective-one-body (EOB) formalism of
conservative dynamics for massless Scalar-Tensor (ST) theories at third
post-Newtonian (PN) order. The nonlocal-in-time EOB Hamiltonian is obtained by
mapping the order-reduced Hamiltonian corresponding to the nonlocal-in-time
Lagrangian derived in [Phys. Rev. D 99, 044047 (2019)]. To transcribe the
dynamics within EOB formalism, we use a strategy of order-reduction of nonlocal
dynamics to local ordinary action-angle Hamiltonian. We then map this onto the
EOB Hamiltonian to determine the nonlocal-in-time ST corrections to the EOB
potentials $(A,B,Q_e)$ at 3PN order.
