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The delayed GeV$-$TeV cascade emission from extragalactic TeV$-$PeV sourcesare regarded as an ideal probe of the inter-galactic magnetic fields. Recently,LHAASO has detected $\sim 10$ TeV emission of the extraordinary powerful GRB221009A within $\sim 2000$ s after the burst. Here we report the detection of a$\sim 400$ GeV photon, without accompanying prominent low-energy emission, byFermi-LAT in the direction of GRB 221009A with the time delay of 0.4 days. Sucha hard spectrum can be generated from electromagnetic cascades initiated byearly primary $\sim 10$ TeV photons in the intergalactic space. Aninter-galactic magnetic field strength of $B_{\rm IGMF}\sim 4 \times 10^{-17}$G, comparable to limits from TeV blazars, can naturally account for the arrivaltime of the $\sim 400$ GeV photon as well as the HAWC non-detection. Such astrength will be stringently tested by the upcoming CTA.

An inter-galactic magnetic field strength of $\sim 4 \times 10^{-17}$ G inferred with GRB 221009A