  A rigorous evaluation of the two-photon exchange corrections to the hyperfine
structure in lithiumlike heavy ions is presented. As a result, the theoretical
accuracy of the specific difference between the hyperfine splitting values of
H- and Li-like Bi ions is significantly improved. This opens a possibility for
the stringent test of the many-electron QED effects on a few percent level in
the strongest electromagnetic field presently available in experiments.
