Let R be a ring. R is right MP-injective, if every R‑monomorphism from a principal right ideal of R to R extends to an endomorphism of R; R is right MGP-injective if, for any  there exists a positive integer n such that  and any R‑monomorphism from  to R extends to an endomorphism of R. It is shown that (1) R is right FP-injective if and only if the full matrix ring  is right MP-injective for every positive integer n if and only if the full matrix ring  is right MGP-injective for every positive integer n; (2) If  is right MGP-injective, then R is right MP-injective.