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For right R-modules M and N, if every monomorphism from a fully invariant M-cyclic submodule s (M) of M to N can be extended to a homomorphism from M to N, then N is called pseudo FI-M-principally injective. If M is pseudo-FI-M-principally injective, thenitiscalledFI-semiinjective. Inthispaper, wediscusssomebeautifulproperties of pseudo-FI-semi injective modules. We also prove that every duo-FI-semi injective module satisfies the summand intersection property (SIP) and the summand sum property (SSP).