This work is aimed at study a lag synchronization of hyperchaotic complex-valued systems, which is motivated by a wide range of applications of this approach in nonlinear sciences (e.g., secure communications, encryption techniques, etc.). A scheme to study lag synchronization of hyperchaotic complex-valued systems is presented. The control functions are analytically derived and the related numerical simulations are carried out to verify the consistency of the scheme. The complex-valued Rabinovich system describing the parametric excitation of waves in a magneto-active plasma is considered as an interesting example to study this kind of synchronization. Based on the complexity of hyperchaotic dynamical systems, which may be useful in secure communications, a corresponding scheme is presented and two types of encrypted messages (plain text and audio signal) are considered as test examples.