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We describe injective endomorphisms of the inverse semigroup B ω F introduced in [Visn. Lviv. Univ., Ser. Mech.-Mat., Issue 90, 5 (2020)] for the case where the family F n is generated by the set {0,1,..., n}. In particular, it is shown that the semigroup of injective endomorphisms of the semigroup B ω F is isomorphic to (ω, +). Moreover, we describe the structure of the semigroup E n d B λ of all endomorphisms of the semigroup of λ × λ -matrix units B λ . [ABSTRACT FROM AUTHOR]