  The dynamics of Hermitian many-body quantum systems has long been a
challenging subject due to the complexity induced by the particle-particle
interactions. In contrast, this difficulty may be avoided in a well-designed
non-Hermitian system. The exceptional point (EP) in a non-Hermitian system
admits a peculiar dynamics: the final state being a particular eigenstate,
coalescing state. In this work, we study the dynamic transition from a trivial
insulating state to an {\eta}-pairing state in a composite non-Hermitian
Hubbard system. The system consists of two subsystems, A and B, which are
connected by unidirectional hoppings.We show that the dynamic transition from
an insulating state to an {\eta}-pairing state occurs by the probability flow
from A to B: the initial state is prepared as an insulating state of A, while B
is left empty. The final state is an {\eta}-pairing state in B but empty in A.
Analytical analyses and numerical simulations show that the speed of relaxation
of the off-diagonal long-range order pair state depends on the order of the EP,
which is determined by the number of pairs and the fidelity of the scheme is
immune to the irregularity of the lattice.
